The Federal Home Loan Bank of Topeka, Kan., has found that a government unit that was created to sell property inherited from failed savings and loans is in serious financial difficulty.

The unit is the Federal Asset Disposition Association (FADA), which was created in 1985 with $25 million in federal funds and a $50 million line of credit guaranteed by the federal government.

FADA was expected to raise money from the sale of property and turn a profit within one year. Instead it is losing more than $1 million a month and ended 1987 $10 million in the red.

The Topeka bank is one of 12 federal organizations created by the Congress to raise money that S&Ls can borrow and then lend to home buyers.

In addition the banks supervise and audit the S&L industry. The Topeka bank has the additional duty of auditing FADA.

FADA is under investigation by two congressional committees, the Justice Department and the Federal Home Loan Bank Board, the agency that created FADA, on allegations of mismanagement and conflicts of interest.

FADA has used half of its $25 million in seed money and has borrowed $6.5 million of its line of credit, which the government extends to it through the Home Loan Bank of Topeka.

FADA denies that it is having trouble activating its remaining $43.5 million line of credit.

But the bank board may be concerned about continuing to guarantee advances from the Topeka bank because some government officials believe FADA is losing too much money to be creditworthy, government sources say.

FADA has billed the bank board for $10 million in fees in an effort to break even for the year. The bill is in hot dispute, with some bank board officials arguing the government should not pay it.

The bill includes $4.5 million in legal fees, which FADA originally agreed the government should not reimburse. The remainder includes fees for managing property for the government.

Some bank board officials dispute the way FADA calculated the bills, saying FADA in effect padded the bill so that the organization could break even.