H1B Dropbox and I797 Near Expiry

H1B in USA on expired H1B Stamped and New approved I-797.
Drop box appointment with 4 months of I797 Expiry.
Is that fine?

Submit a new DS-160 referencing the new extended I-797. Update the appointment in the CGI portal with the new DS-160 or just call VFS and they can help update.

will there be any problem for Drop box appointment with I797 which will expire in 4 months.

No issues but you may get visa with a short validity. Ideally you should have extension of status approval and then go for stamping.