Profits of Maryland's largest banking firm, Maryland National Corp., soared 48 percent to record levels in the first quarter of 1981. Earnings of Riggs National Bank of Washington, however, were only slightly above the same period last year.

Separately, Avemco Corp. of Bethesda also reported record quarterly profits, while First American Bank of Washington reported a modest first-quarter increase and NS&T Bank of Washington listed a substantial gain.

Maryland National operating earnings in the recent quarter, not counting securities transaction gains or losses, were $10.3 million ($1.36 a share) compared with $6.2 million (86 cents) a year earlier. The first-quarter profit were the highest in any three-month for the company, which owns Maryland National Bank.

Chairman Robert D.H. Harvey noted yesterday that interset income on loans was substantially higher and that nonbank subsidiaries had contributed higher profits.

"Though the corporation's earinings were benefitted by approximately $1.4 million resulting from mandatory redemption of certain Penn Central securities during this quarter, we are still more than satisfied" with the increase that would have taken place without the Pennsy situation, he added.

Assets of the region's largest bank firm rose to $3.7 billion from $3.6 billion a year ago, deposits rose slightly to $2.63 billion, and loan volume expanded to $2.4 billion from $2.28 billion.

Riggs National Bank, the largest in Washington, reported first-quarter earnings of $5.5 million ($1.84 a share) compared with $5.3 million ($1.82) a year ago. The results include a wholly owned subsidiary, Central Charge Service.

Chairman Vincent C. Burke Jr. said yesterday that employe benefit expenses were up appreciably in the first quarter, including costs of a new dental plan. "But I'm pleased with the overall picture. It was a good quarter," Burke added. Assets of Riggs rose 18 1/2 percent to $3.24 billion, deposits were up about 17 percent to $2.62 billion, and loan volume grew by 11 percent to $1.55 billion.

First American Bank N.A., the District flagship of the Financial General Bankshares holding company, reported first-quarter profits of $1.7 million (74 cents) compared with $1.6 million (69 cents) last year. Assets rose to $699 million from $659 million, while deposits increased by 6 percent to $569 million.

NS&T Bank, the new name of National Savings & trust Co., listed first-quarter profits before securities transactions of $1.17 million ($2.55 a share) compared with $834,000 ($1.82) a year ago. Deposits rose about 3 percent to $410 million. Directors declared a regular quarterly dividend of $1.20 a share, payable May 1 to owners of record April 24.

Wapora Inc., a Chevy Chase environmental and energy research firm, reported earnings of $176,552 (29 cents) in the nine months ended March 31 compared with $127,436 (21 cents) a year earlier as sales expanded to $5.85 million from $4.89 million.