I am looking for a fruiting vine that can climb a fence and live in afternoon shade. By fruiting, I mean something that I can eat! Any suggestions?

Grapes.

Anything else? How well do peas grow in partial shade?

Are you wanting something that stay green all year, or at least comes back every year? Then peas are not the answer. The vine will grow in partial shade but you probably will not get many blooms/peas from it.

I just want it green in summer. Thank you all for your responses!

You might also give pole beans, cucumbers, malabar spinach or a thornless blackberry. I don't know what partial shade exactly means but the first three are cheap annuals that won't cost you much to experiment with.
Tony M

Hyacinth bean might work