1
My jacket was on the chair. I was cold, so I put on it.
My jacket was on the chair. I was cold, so I put it on.
You can say ‘put on your coat’ or ‘put your coat on’. But if you use a word such as it or them instead of naming the clothes, put it between put and on: ‘Put it on.’ ‘Put them on.’
2
I putted on my jacket and went outside.
I put on my jacket and went outside.
The past form of put is put, not putted. Use put on when you place clothes on your body. Use wear when the clothes are already on your body: ‘I put on my jacket in the morning.’ ‘I wore it all day.’
See WEAR