I have a 12v 900 CCA AGM Battery for 12v inverter my solar controller full charge the battery but over night the battery drop to 10.8volts is the battery faulty
I had this battery is new and I had it for 12 months
the solar controller will not over charge the battery
The CCA (Cold Cranking Amps) rating suggests you bought the wrong battery for the application. You bought a CAR type battery which will not survive a deep discharge. The plates are too close together.
AGM batteries are very finicky about over charging. They don't like it. Unless you have a charge controller with a setting for AGM, use flooded or gel. You also want to look for the deep cycle label