The Treasury sold $3.5 billion of two-year notes at a record average yield of 15.01 percent at yesterday's monthly auction.

The agency received $6.91 billion in bids for the notes, and accepted those at yields ranging from 14.94 percent to 15.07 percent, including $819 million of non-competitive bids at the highest return. The agency accepted 15 percent of bids at the highest return. The coupon interest rate on the notes will be 15 percent.

The $3.5 billion in accepted bids includes $290 million of bids at the average price from Federal Reserve Banks acting as agents for foreign and international monetary authorities. Those bids were in exchange for maturing securities.

In addition the agency accepted $500 million of bids at the average price from government accounts and Federal Reserve banks for their own account in exchange for securities maturing March 31.

The Treasury also announced plans to sell $15.5 billion in securities over the next several weeks to raise needed cash.

The announced sales were:

$4 billion in 359-day Treasury bills to refund $3.3 billion of bills maturing April 1 and to raise $700 million in new cash. Tenders will be received up to 1:30 p.m. next Wednesday.

$5 billion of 77-day Treasury bills to be issued on April 3, representing an additional amount of bills maturing June 19. Tenders will be received up to 1:30 p.m. next Thursday.

$1.5 billion of 15-year, 1-month bonds to be issued April 8 and to mature May 15, 1995. Tenders will be received up to 1:30 p.m. April 2.

An auction on April 1 of about $5 billion in 83-day Treasury bills to be issued April 4, representing an additional amount of bills maturing June 26, 1980. The actual amount of this sale will be announced next Thursday.

The Treasury also said it sold $6 billion in 37-day cash management bills yesterday at an average return of 16.122 percent.

The agency received $8.5 billion in bids for the bills and accepted those at returns between 15.723 percent and 16.725 percent. The agency didn't accept noncompetitive bids. It accepted one percent of bids to the highest return. The coupon equivalent rate was 16.62 percent.

The agency said an additional $900 million of bills will be issued to Federal Reserve banks as agents of foreign and international monetary authorities for new cash.