With a flood of Cuban and Haitian refugees focusing new attention on the Caribbean, the Carter administration is considering some potentially controversial changes in aid policy toward the region known as "America's third border."

The most sensitive of the ideas under study would involve attempting to expand U.S. military assistance activities to include training and equipment for the police forces of the Caribbean's island republics. Such aid currently is prohibited by law.

In addition, the administration is debating whether U.S. development assistance to the Caribbean, much of whch is now channeled through multinational lending agencies, should be put on a direct, country-to-country basis that would give the United States more leverage and visibility in the struggle to overcome the region's econonic problems.

Prompting these questions is the administration's concern that the Caribbean's massive economic difficulties will produce widespread political instability in the region and that U.S. aid is not being employed in a manner most effectively calculated to head off potential crises.

In its most obvious terms, that concern has been given flesh-and-blood form by the torrent of Cuban and Haitian asylum seekers pouring into the United States. Among many U.S. officials, there is fear of the phenomenon spreading and causing a swelling army of the jobless or oppressed from other Caribbean islands seeking to follow in the wake of the Cubans and Haitians.

An even more immediate concern is that Cuban President Fidel Castro, to divert attention from his internal problems, may embark on a new campaign of anti-American confrontation that would include attempts to exploit the shakiness of many Caribbean governments and bring them into the sphere of Cuban influence.

These concerns did not begin with the sealift of Cuban refugees that sprang into being in late April. In actuality, the Carter administration has had an on-again preoccupation with the Caribbean that started to become intense in March 1979, when a coup in the tiny eastern Caribbean island of Grenada brought a strongly pro-Cuban government to power and triggered fears of a ripple effect through the region.

For a brief period following the controversy late last summer over a Soviet combat brigade in Cuba, the Caribbean stood close to the top of the administration's foreign policy agenda -- a status certified by President Carter's nationally televised Oct. 1 speech pledging a series of major U.S. military and economic initiatives in the region.

However, that emphasis quickly was replaced by the diversion of the administration's attention to the twin crises in Iran and Afghanistan, and the Caribbean almost overnight faded out of the headlines and the attention span of senior administration policymakers.

In the intervening months, however, the region has seen a number of events -- financial chaos in Jamaica, a military coup in the former Dutch colony of Surinam, continuing outbursts of labor and political strife in some of the eastern Caribbean ministates -- that have served to strengthen fears of a potentially explosive situation building up in America's back yard.

The Caribbean still hasn't moved back into the front rank of policymaking attention. But these events, coupled with the publicity impetus provided by the exodus from Cuba, have convinced some influential administration officials and members of Congress that the time is ripe for a serious, far-reaching reexamination of U.S. policies and activities in the Caribbean area.

Rep. Dante B. Fascell (D-Fla.), whose base in the Miami area has made him the unofficial point man for the administration in congressional actions involving the Caribbean, says: "The wheel is squeaking down there right now, and that's when Congress perks up and becomes receptive to calls for new initiatives. It's a good time for the administration to be looking ahead and coming up with some ideas."

Part of this reexamination includes a moving away from the traditional tendency to think of the region in terms of a "Caribbean basin" that includes not just the islands but also Mexico, Central America and northern South America.

Although, there are interrelationships, Central America, with its tradition of military dictatorship and leftist guerrilla insurgency, poses a set of problems far different than those of the chain of islands stretching 2,000 miles through the Caribbean Sea from the Bahamas to Trinidad.

Most are former British colonies operating on the "Whitehall system" of parliamentary democracy and are steeped in traditions of language and culture that set them far apart from their Spanish and French-speaking neighbors.

While Grenada demonstrated that these countries are not immune from the "coup syndrome," their most immediate problems are economic. Most are relics of old plantation economies; and, in the vacuum left by Britain's withdrawal from the region, they are plagued constantly by the need to try to preserve democratic institutions with resources so insufficient for their growing populations that some have habitual unemployment rates of up to 50 percent.

As Fascell sums it up, "For enormous numbers of people down there, there's no way to make a living, and that leaves them with two choices: they can try the illegal immigration route and hope they'll make it to Florida, or they can stay put and listen to the blandishments of agitators claiming to have ideological panaceas that will work better than democracy."

The same points were made by former under secretary of state Philip C. Habib in a confidential report written last fall at the request of then Secretary of State Cyrus R. Vance. In it, Habib said the chief threat to the United States in the Caribbean is "economic and social instability" that is creating "targets of opportunity" for Cuba to extend its influence through the region.

Habib concluded that the best way for the United States to counter the danger lies not in a stepped-up Caribbean military presence but in better use of U.S. economic aid and political cooperation to help the countries of the area overcome their development and employment problems.

In line with Habib's recommendations, current U.S. policy stresses easing economic instability by trying to prod the polyglot collection of former British, Spanish, French and Dutch islands to pull together in greatly accelerated regional cooperation schemes.

Because the amount of aid that the United States can commit falls far short of the region's needs, the administration has put great emphasis on what one official calls "the godfather role" of the Caribbean Group for Cooperation in Economic Development. This is an umbrella organization of aid-donating countries and financial institutions whose collective pledges to the region jumped from $220 million in 1977 to $612 million last year.

But, within these broad policy outlines, a lively debate is under way in the administration about whether the U.S. practice of restricting direct aid for individual countries to so-called "humanitarian needs" and channeling other assistance through international lending agencies is working effectively in the Caribbean.

In its aid request to Congress for fiscal 1981, the administration asked for $134.6 million for development assistance to the Caribbean. Of that, roughly $100 million involves bilateral aid (primarily for the Dominican Republic, Haiti and Jamaica), and $34.4 million would be filtered through the Caribbean Development Bank mostly to promote regional cooperation.

However, many people, including Fascell, who recently toured the eastern Caribbean, think the United States relies too heavily on the bank, whose cumbersome bureaucratic processes often are slow to put the money to work and also submerge awareness of the United States as a major donor.

Fascell notes that Cuba reaped a tremendous harvest of favorable attention in the region through the relatively inexpensive move of sending a few doctors and medical technicians to help the new government in Grenada and then providing some aid to build a new airstrip there. He believes the United States can learn a lot from that example.

"Instead of relying so much on the Caribbean Development Bank, we should be putting much more emphasis on direct aid projects -- things like fisheries or solar energy development -- that would get the money out faster, have a more immediate impact on problems that affect people's everyday lives and make the United States much more visible," he says.

A potentially more controversial aspect of the aid debate involves security assistance.In his report, Habib is known to have cited the need for Washington to focus more closely on problems of internal security and "ideological direction" in the English-speaking Caribbean.

By that, he meant that many countries have been left vulnerable to outside subversive pressures by weak, ineffective police forces whose training and equipment needs lie outside the normal range of U.S. military assistance. aIn fact, Congress, reacting to past abuses in countries with repressive regimes, has banned the use of U.S. aid to assist police forces.

Some senior administration officials, such as Matthew Nimetz, under secretary of state for security affairs, are known to believe that this policy, however well-intentioned, actually works against U.S. efforts to strengthen democratic governments in the Caribbean.

The administration already has instituted a small military assistance program to help Barbados and the tiny neighboring islands of St. Lucia, St. Vincent and Dominica improve their coastal patrol abilities to combat smuggling, gun running and drug trafficking.

However, this is regarded as only a small beginning in meeting the specialized security needs of the islands, and Nimetz and his staff are known to be wrking on a proposal to overhaul U.S. security assistance programs that could include an attempt to induce Congress to make changes in the law that would permit help to selected Caribbean police forces.

Such a move is certain to provoke opposition, particularly from human-rights advocates who would view it as a dangerous precedent. But many administration officials, increasingly convinced that this is an important part of coping with the problems of the Caribbean, feel strongly that the attempt should be made.