Vincent's NT Word Studies
22. For (gar). Your determination to be under the law is opposed by Scripture, if you will understand it, for it is written, etc.A bondmaid (thv paidiskhv). The bondmaid, indicating a well known character, Hagar, Gen. xvi. 3. The word in Class. means also a free maiden; but in N.T. always a slave. So almost always in LXX; but see Ruth iv. 12; Judith xii. 13.
Robertson's NT Word Studies
4:22 {By the handmaid} (ek tes paidiskes). From #Ge 16:1. Feminine diminutive of pais, boy or slave. Common word for damsel which came to be used for female slave or maidservant (#Lu 12:45) or doorkeeper like #Mt 26:29. So in the papyri.