Allegheny Beverage Corp. and Best Products Co. yesterday reported increased profits in the July-September quarter while Kay Corp., an Alexandria jewelry retailer and trading company, listed a substantial decline in earnings for the recent quarter and a net loss for the first nine months of 1981.

Baltimore-based Allegheny, a major bottler of Pepsi-Cola and other soft drinks, said profits in the third quarter rose to $2.2 million (56 cents a share) from $1.8 million (47 cents) in the 1980 period, as sales soared to $111 million from $40 million--a large gain that reflects the acquisition earlier this year of Macke Co., a food services, vending and office furnishings firm based here.

For the first nine months, Allegheny earned $5.8 million ($1.48) versus $4.3 million ($1.13), and sales increased to $307 million from $105 million. The 1981 results include Macke operations on an equity (stock investment) basis prior to the Jan. 30 formal takeover and on a consolidated basis thereafter. Macke's Desks & Furnishings office-furniture division turned in the company's best profit gains, Allegheny said.

Chairman Morton Lapides added yesterday that Macke has continued to generate profits at a "very good rate" while a price war among soft drink bottlers has led to "disappointing results" in that business. Allegheny's Pepsi-Cola bottling subsidiary is currently engaged in a bitter court battle with a major Coca-Cola bottler, Mid-Atlantic Bottling Co. of Richmond, in which both sides are alleging antitrust violations at a jury trial in Norfolk.

Best Products of Richmond, the nation's largest catalogue-showroom merchandiser, announced an increase in earnings for its first fiscal quarter and raised quarterly dividends at its annual stockholders' meeting yesterday.

Profits climbed 11 1/2 percent for the quarter ended Oct. 3 to $2.7 million (27 cents) from $2.4 million (25 cents) for the comparable period of 1980. Sales grew 26.6 percent to $237 million from $187 million last year. For the year to date, Best sales were $319.4 million compared with $262.1 million by this time last calendar year, a 21.9 percent gain.

Since January, Best has opened 16 new showrooms, including one in Fairfax County and one in Bethesda, bringing its total to 100. Because of this expansion, Best announced "comparable showroom sales," which indicated a gain of 12 percent for the first quarter of the new fiscal year and 8.7 percent in the calendar year. For October, the first month of the holiday sales season, Best sales were $82.9 million, up 10.2 percent from $75.2 million last year, according to Best representative Mike Welton.

The firm's quarterly dividend will grow to 8 cents a share from 6 cents, payable Dec. 15 to shareholders of record Dec. 1.

Kay Corp. reported third-quarter profits fell to $901,000 (25 cents) from $5.3 million ($1.49) in the same period last year while revenues declined to $137 million from $231 million. For the first nine months, Kay listed a net loss of $10.16 million on sales of $477 million compared with earnings in the 1980 period of $4.3 million ($1.17) and sales of $700 million.

The reduced profitability and lower revenue volume reflect, in part, the sale of some assets of a subsidiary. Kay directors approved a regular quarterly cash dividend of 18 3/4 cents a share, payable Dec. 15 to owners of record Nov. 30.

Hittman Corp. of Columbia, a diversified environmental and energy-research services company, reported third-quarter profits rose to $200,500 (19 cents) from $158,400 (15 cents) a year earlier as sales declined to $5 million from $5.8 million. Nine-month profits rose to $634,500 (61 cents) from $287,100 (28 cents), and sales increased to $17 million from $15 million.

American Indian National Bank of D.C. reported record earnings for the first nine months of $587,573 ($2.55) compared with $336,203 ($1.46) in the 1980 period. Average deposits jumped 70 percent to $24.5 million from $14.5 million while assets soared to $33 million from $17 million.