These are your choices.
As Ryder--173rd Ohio Infantry Regiment (can't find in roster)

As Rider, these choices
Company B, 104th Regiment, Pennsylvania Infantry
181st Regiment, Ohio Infantry (can't find him in roster)
202nd Regiment, Pennsylvania Infantry (can't find in roster)

Pennsylvania does not list age in their rosters.
I could not find a Jacob Rider in 1890 US Veterans Census that might apply

I don't think these units apply
150th Regiment, Indiana Infantry (listed as Reider)
31st Regiment, Iowa Infantry died of wounds in 1864
8th Regiment, Kansas Infantry died of wounds in 1863
31st Missouri Infantry Rgt. burial location known
9th Regiment, Ohio Cavalry 1846 born
60th Regiment, Ohio Infantry 1838 born
80th Regiment, Ohio Infantry 1843 born
132nd Regiment, Ohio Infantry (National Guard) 1845 born
176th Ohio Infantry Rgt. burial location known
49th Regiment, New York Infantry 1845 born
143rd NY Infantry Rgt. died in 1864 or earlier
168th Regiment, Pennsylvania Infantry (Drafted Militia) burial location known
208th Regiment, Pennsylvania Infantry about 1896 died