What do I do with the tenants belongings who is incarcerated and has no others to pick it up

Similar to when a tenant dies I believe. Some states require a certified letter to be sent to the next of kin, and after a number of days have passed you can dispose as you see fit. In this case possibly a letter to the former tenant at his new address. It is certainly unreasonable to expect the landlord to absorb cost of storing the belongings or not being able to rent the apt. Try searching your state's law by entering "dispose of tenant's property in (name of state)" or something similar, or you may have to consult an attorney.