I note from the spelling of the name (Avent-Avant-Aven-Avens) that you have the Aven variety---which is normally attributed to Amos Aven from Chatham Co. NC to Carroll Co. - Henderson Co Tn. (Same place, line changes)
His family in the next generation, migrated to parts of Miss. If you will tell me WHERE, I might can tell you which branch.. What years etc..whatever you can.
Also, Benjamin Avant was also in Ms..but used that spelling. He had numerous children by two wives.