I filed for divorce from my husband in New Jersey. iIf I take out a mortgage to buy a house for me to move to, could my current husband have a claim

Ordinarily anything that you gain as an asset or a liability after filing for divorce is no longer considered marital property. So while money that you are putting up toward the house may or may not have been equitable income, the house itself is being purchased post date of the complaint and would not be subject to a claim.