Can one start the aircraft's(commercial/fighters) engine midair at high altitudes especially turbojet or turbofan engines?
As long as there is engine (e.g., N1) rotation, no structural damage, no fire, etc., generally speaking an in-flight restart may be attempted.
There are certain guidelines/conditions that control whether the re-start attempt can be done with a windmilling engine or if a cross-bleed start (using air from the other engine to rotate the failed engine for starting purposes) needs to be done. (other conditions that must exist are shown in the in-flight restart procedure available to the crew).
The aircraft manufacturer typically provides an In-Flight restart procedure published in the QRH (Quick Reference Handbook) or Emergency Checklist.