What is UE Context Modification Request in 5G NGAP?

It is the AMF-to-NG-RAN message used to partly modify an already established UE context.

What are the mandatory IEs in UE Context Modification Request?

AMF UE NGAP ID and RAN UE NGAP ID are mandatory so NG-RAN knows exactly which live context to update.

Does this message always carry every context field again?

No. It usually carries only the specific optional IEs that AMF wants NG-RAN to change.

When should engineers prefer modification over release and rebuild?

Use modification when the context is still valid and only selected parameters need adjustment; use release and rebuild when the context itself is no longer trustworthy.