THE BATTLE IS ON — Sherri Shepherd will FIGHT her estranged husband tooth and nail to get CUSTODY of their unborn child … this according to prenup docs obtained by TMZ.

Sherri filed divorce docs earlier this month, days after hubby Lamar Sally filed his own docs for legal separation where he asked for full custody of their unborn child, who is being carried to term via surrogate. The baby is due in July.

Sherri strangely doesn’t even mention custody in her divorce docs, but DOES ask to enforce their prenup … and now we know the prenup is Sherri’s secret custody weapon.

Under the prenup, Lamar agrees that the new kid will live with Sherri and her son Jeffrey from a previous relationship. So the prenup gives Sherri full physical custody of the new baby.

In Lamar’s legal docs, he’s asking the judge to throw out the prenup on grounds of fraud. If he gets the prenup invalidated, that clears the way for his demand for full custody. But proving fraud is hard.

By the way … there’s another reason Lamar wants to invalidate the prenup. It only gives him one lump sum payment of $60K. According to the prenup docs, Sherri raked in $1 million in 2010 (and we know she got raises since then). By contrast, Lamar made $30K in 2010, and $9,000 was from unemployment. So if the prenup goes out the window, Lamar could score big in spousal support.