I'm building a shed with board & batten siding,can I use pressure treated plywood if so what size should I use 1/2,5/8,or3/4" ?

You did not tell us much about the shed such as height and length but 1/2" under the siding should be fine.

I was thinking of using the plywood for the board part of the board and batten,the shed is 10X16 I will probably use a dark stain. What type of plywood & what thickness should I use?