A sitting U.S. president can not be indicted for federal crimes as a matter of constitutional separation of powers and DOJ policy, among other reasons.
The president's constitutional protections and powers (e.g., pardon power, etc.) do not extend to the state level. For example, POTUS can pardon people (including himself) on federal crimes. But can not pardon people for state crimes.
Now imagine a scenario where a POTUS, while sitting in office, is indicted by a particular state Attorney General for a crime, say murder, under state statutes. In that scenario, can POTUS be tried, convicted and jailed for those crimes without being impeached?
As a practical matter, could it actually happen? How would it actually play out given the supremacy clause and other practical considerations of jailing the chief federal executive?
I do not think this question is a duplicate of Can a sitting president of the United States be indicted by one of the states?. That question is limited to the issue of indictment only. This question assumes indictment powers and deals with trial, conviction and, most notably, imprisonment. Given the existing answer to that question, these differences seem relevant and could lead to different or more qualifications on the existing answer.
And, finally and perhaps more importantly, this question also seeks to extract the details of the logistics of how an arrest and/or jailing and imprisonment might or might not be feasible and/or actually occur.