Pictures with Links on widget position

Hello everybody,
I have a problem, I need for my client make special post type, which will show on “widget position”, because on his old web he had it, but I havent the acces ?? ..
I am new in WordPress, so I havent a experiences to solve it myself ??
So I need, own pos type “Partners and sponsors” where client can himself create a post where will be only picture with link and this kind of the post show it in widget (maybe according category).

Plase anybody have an idea how to do it? I will be really glad.
Thanks you.