How would I file taxes if my spouse was incarcerated for all but 3 months of the year? We usually file married filing joint.

You can still file a joint return as long as your spouse agrees to file that way.  By filing a joint return you will get the married filing jointly standard deduction of $29,200 and the child-related credits like earned income credit if you are eligible.   

It is always allowed to file jointly if you are legally married if you agree to do so, even if you are living apart for some reason.  Joint filing almost always results in lower taxes, for various reasons.