One of two companies competing for the valuable Fairfax County cable television monopoly has added some new political muscle in its bid to win the county franchise this summer.

Fairfax Telecommunications, which already had the county's senior state senator as general counsel, last week released a list of new investors and many of them have political ties to the county supervisors who will award the franchise. Included in the stockholders list are former Virginia attorney general Andrew P. Miller, a former United States treasurer, the current county Democratic chief and the 23-year-old daughter of Gov. Charles S. Robb's campaign finance chairman.

If Fairfax Telecommunications, actually a partnership between local investors and a large Colorado cable firm, wins the franchise, the local stockholders are virtually guaranteed handsome profits.

"I think the big cable companies are hoping to use these people to lobby," said Supervisor Audrey Moore, a Democrat. "I just wish these local people weren't involved." At least three members of the Democratic Committee in Annandale, Moore's district, have invested in Fairfax Telecommunications.

"We were trying to get people that we thought were important people in the community," said Fairfax Telecommunications President L. Gary Byrd, himself a past president of the county Chamber of Commerce and Board Chairman John F. Herrity's appointee to the county Human Rights Commission. "We want to demonstrate to the county board that we are a responsible, capable group that can keep its commitments."

Fairfax Telecommunications is seeking a cable television monopoly throughout most of the county for 15 years. Its 215 local investors, who have paid an average of about $4,000 each, would not have to invest another penny and would own 51 percent of a cable system that could, according to a county study, be worth $260 million at the end of the franchise period.

The minority interest in the partnership is held by Tele-Communications Inc., a Denver firm which controls more than 300 cable systems and claims to be the nation's second-largest cable operator.

In its previously filed application, Fairfax Telecommunications noted that it had offered its stock to any Virginia residents through advertisements placed in The Fairfax Journal. It said this public offering and its requirement that all stockholders "pay cash" for their shares prevent it from being subject to charges of "renting" prominent citizens as lobbyists for the franchise.

"It seemed to us as a family that it would hopefully be a good investment," Fairfax Democratic Party chief Dottie Schick said yesterday. Schick bought $3,000 of stock with her husband and son. She said her position in county politics is not relevant to the purchase.

"I'm not trying to hide it, but I'm not trying to put any pressure on anybody," Schick said. "If you want to have it controlled by people in the county, you're going to have people the supervisors know. You can't have it both ways."

The Democratic Party, which holds a 5-to-4 majority on the county board, is well represented at Fairfax Telecommunications. Miller invested $15,000 after Cross County Cable Ltd., another cable TV firm he had represented, decided not to bid in Fairfax, and Democratic state Sen. Adelard L. Brault, another investor, will receive a $40,000 lump sum payment in stock or cash if Fairfax Telecommunications wins.

The firm is bipartisan. John J. Papajohn, a lawyer and former Republican activist, is a major investor, as is Steven P. Horvath, owner of Tysons Toyota and a contributor to Herrity and Republican Reps. Stanford Parris and Frank Wolf.

Media General Inc., a $367 million Richmond-based communications company, selected only five Fairfax investors, including three prominent members of the county's powerful builder-developer community. All five will be given two shares of stock for each share they buy, or an estimated $4 million for a $2 million investment, if Media General wins.

Fairfax Telecommunications has sought a broader base and now includes among its investors Azie Taylor Morton, who was U.S. treasurer under President Carter; Janine Vitray, the 23-year-old daughter of Fairfax Electoral Board Secretary Jane Vitray, Robb's former finance chief; a past chairman of the Federal Communications Commission, Frederick W. Ford; a past school board member and a past president of the Fairfax Federation of Citizens Associations; two former state legislators, Richard Ryder and Raymond E. Vickery Jr.; a past Republican state Senate candidate, John Watkins; a past finance chairman for former congressman Herbert E. Harris; Dr. W. Leonard Weyl, a Republican who sits on the Virginia Board of Health; and at least six members of the Democratic county committee.

"The county from the beginning has hoped there wouldn't be this kind of local participation," Moore said. Republican Supervisor Marie Travesky agreed: "It's going to make it difficult for a lot of board members to vote on this." CAPTION: Picture, ANDREW P. MILLER . . . put $15,000 in Fairfax Telecommunications.