The South was rebuffed in the Senate yesterday in an effort to alter the government formula for dividing up $2.6 billion in education funds each year, but came away with a $20 million consolation prize.

The Senate rejected, 60 to 35, an amendment by Dale Bumpers (D-Ark.) to the supplemental appropriations bill that would have increased the South's share of so-called Chapter I funds for the educationally disadvantaged.

The existing formula, which the South was instrumental in writing in 1974, allocates funds according to numbers of children living below the federal poverty level, plus each state's average education expenditure per child. Until now it has been based on 1970 census data, but this year it will shift automatically to the 1980 census. Because the South had fewer children in poverty in 1980 than in 1970, many southern states will lose money as a result of the shift.

Bumpers thus proposed altering the formula to give weight to state per-capita income. This remains low in most southern states, and would have meant larger grants for almost every southern state and losses for many in the North.

But education subcommittee Chairman Robert T. Stafford (R-Vt.) and others fought Bumpers and won, after first agreeing to provide about $20 million extra this year for southern states that might otherwise lose money.

The Senate also:

Approved by voice vote a John Heinz (R-Pa.) amendment barring the Social Security Administration from removing mentally ill persons from the disability rolls for the next six months, and ordering Social Security to revise its standards for judging whether the mentally ill are able to work.

* Approved, 75 to 23, a proposal by Sen. Daniel P. Moynihan (D-N.Y.) to add $225 million this year for health benefits for unemployed workers once a basic authorizing bill is passed.

* Approved an amendment proposed by Sen. Howard M. Metzenbaum (D-Ohio) barring the government from repaying any company for loss of tax breaks involved in government leasing contracts.