Jeffrey N. Cohen, a local real estate developer, has purchased about 25 percent of the outstanding shares of District of Columbia National Bank, a deal that makes him the largest single holder of the institution's stock.

Cohen said yesterday that he purchased more than 50,000 shares of the stock, a transaction worth about $1.6 million, based on the stock's recent bid price in the over-the-counter market.

Cohen, 30, also was named to the bank's board of directors. His father, Norman C. Cohen, has been on the board since 1966.

In an interview yesterday, Jeffrey Cohen, a long time friend of the family of S. Greenhoot Fischer, D.C. National's chairman, said he had made the purchase because the bank's stock is a good investment. In addition, Cohen said he is "interested in getting involved with the bank in the future." c

According to the 1979 proxy statement of D.C. National, Fischer held 24,139 shares of the bank's stock, or 12.1 percent of the outstanding shares.

Neither Fischer nor Thomas Condit, the bank's president, sold stock involved in the purchase. Condit said. Cohen would say only that the stock was purchased by a small group of individuals.

In recent years, D.C. National has been one of the city's fastest growing banks. Last year the bank reported profits of $689,000, a 51 percent increase over 1977, a rate of gain the company said was the largest reported by a D.C. bank.

Further, D.C. National also reported a 22 percent increase in assets in 1978, and has announced an 83 percent increase in profits for the first half of 1979.

Cohen, a native of the District, and a Catholic University law school graduate, is a member of the D.C. General Hospital Commission and the president of the Jewish National Fund.

He has been involved in several development projects in the Dupont Circle area, including a building at 1636 Connecticut Ave. NW, which once housed Ellen's Irish Pub.

Cohen praised the bank's management and said he did not expect any changes at the bank to result from his purchase and his membership on the D.C. National board.