Middle English biyeten, from Old English begietan (West Saxon), bigetan, bigeotan (Anglian) "to get by effort, find, acquire, attain, seize" (class V strong verb, past tense begeat, past participle begeaton), from be- + get (v.). The sense of "to procreate" is from c. 1200, generally used of the father only. Similar formation in Old Saxon bigitan, Old High German pigezzan, Gothic bigitan "to get, obtain." Related: Begot; begotten.
<a href="https://www.etymonline.com/word/begetter">Etymology of begetter by etymonline</a>
Harper, D. (n.d.). Etymology of begetter. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/begetter