Bolstered by the boom in small cars, American Motors Corp. reported record profits from continuing operations of $68.1 million in its latest fiscal year.

AMC, the smallest of the major American automakers, said its fiscal fourth-quarter profits fell 59 percent from a year earlier, but the decline was not nearly as great as those suffered by its three big competitors in the three months.

The company said its sales in both the quarter and year set records, at $831.3 million and $3.17 billion. Sales for fiscal 1978 were $2.585 billion, with some $682.7 million in the third quarter.

AMC's new-car sales jumped 14 prcent in October while those of General Motors Corp., Ford Motor Co. and Chrysler Corp. dropped sharply. Sales of small, fuel-efficient cars contributed to its excellent fiscal-year results, AMC said. The company began sales last month of the only domestically made four-wheel-drive car, the Eagle.

AMC Chairman Gerald Meyers said he was confident about the company's future, especially because of its alliance with the French automaker Renault. Renault recently purchased a 5 percent stake in AMC and is set to increase its interest to 22.5 percent.

Meyers said in the earnings statement that " restructured automotive operations were solidly profitable. The company's products were properly postioned to meet the strong demand for smaller, economical passenger cars."

Meyers said the year's results were helped by a "strong performance" overseas, and AM General, AMC's military truck subsidiary, was "profitable with record sales of $504 million."

His remarks about profitable automotive operations were somewhat of a surprise because several analysts had said AMC cars were just breaking even -- itself an improvement from years of heavy losses. AMC has consolidated its car lines in a single assembly plant in Kenosha, Wis., and dropped all but compact and subcompact lines.

AMC's $68.1 million in profits from continuing operations in fiscal 1979 came before a special gain of $15.8 million from tax credits. It surpassed results for the company's previous best year, 1959, by $18.6 million.

Profits including the special gain totalled $83.9 million ($2.76 a share), better than double the $36.7 million ($1.21) of fiscal 1978.

AMC earned $10.6 million (ok cents) in the fiscal fourth quarter ended Sept. 30 compared with $26 million (86 cents) in the same period a year earlier.

The 59 percent drop compared with declines of 96 percent at GM and 66 percent at Ford, and a record loss of more than $460 million at troubled Chrysler.