Hi all need some help if possible. Bought a 05 lancer abit ago and it's losing battery power.

So I bought a brand new alternator and got it installed thinking that would work...nope.
just bought a brand new battery and same thing.
what's going on is I can jump the car and she will hesitate for a second but start. She drives fine no battery light comes on nothing. When i shut it off then start again right away she comes on no problem but after sitting for say 10 mins she hesitates again but will just start after like 5 seconds.
if she's left over night shes dead nothing have to jump it.
I put a volt meter to it and with the car off after driving she's at 12.5v but slowly goes down. When I start her she drops to 11v then comes back up to 13.5ish and then stays between 12 and 13. Sometimes she jumps to 14 but never stays.
please help I'm have some mechanical skill but this just confuses me. Thanks