Saying he wished to deter other potential offenders, a D.C. Superior Court judge yesterday sentenced Andrea J. Johnson, 23, to serve 24 days in jail for defrauding the District's unemployment compensation system of $1,322.

Johnson is the first person to be jailed in connection with a crackdown on unemployment compensation fraud that began last spring, according to officials of the D.C. unemployment compensation board.

Judge Samuel B. Block sentenced her to a one-to-three-year term. He then suspended all but 24 days of that, and ordered that the 24 days be served at the rate of two days a week over the next 12 weeks.

Block also ordered Johnson to repay the $1,332 she wrongfully received in unemployment payments. She received benefits of $111 a week, between October, 1975, and January, 1976. During that time, she was earning $125 a week working in the office of a physician.

The judge said he hoped Johnson of 1644 Park Rd. NW, would continue working for the physician while she serves her sentence and repays the money.

Johnson was among 28 persons indicted by a federal grand jury last October on charges of fraudulently receiving unemployment compensation. The indictments alleged that $56,000 in fraudulent claims had been paid to the defendants.

On Dec. 16, Othel C. Yancey, 30, of 4242 Suitland Rd., Suitland, was given a 6-to-18-month suspended sentence by Superior Court Judge John R. Hess. She also was ordered to return $3,661 in payments.

Officials of the compensation board said they believed that fewer than 1 per cent of the 16,000 persons now receiving benefits were involved in fraud.