The former PTA treasurer of a sought-after Brooklyn public school could get a jail-free plea deal on charges she looted the organization’s funds to finance fertility treatments.

Providence Hogan, 44, made a brief appearance in Brooklyn Supreme Court yesterday, after which her lawyer, Stephen Flamhaft, said she would be required to pay back the nearly $100,000 she is accused of filching from the PTA of PS 29 in Cobble Hill.