If my opponent attacked me with one character with deadly during a military challenge and I defend the challenge with one character and lose can I kill the character who defended the challenge for the military claim before I kill him with deadly?

If my opponent attacked me with one character with deadly during a military challenge and I defend the challenge with one character and lose can I kill the character who defended the challenge for the military claim before I kill him with deadly?

Yup. Claim happens during the framework action "Resolve claim", while deadly happens as a passive after you've awarded renown. It's quite common to block with a chump whom you'll chose to die for military claim, making deadly less effective in military challenges than in power/intrigue.

Keep in mind that if you had two defending characters, you'd have to chose the remaining (living) character to die to deadly, not the one you chose to claim.