Please anyone guide me how I can edit and update my OSM map which is running on my ubuntu server

Are you asking how to change the style of the rendered map, or how to update it as people update OSM, or how to add new things to it (that don’t beling in OSM)?

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Is you Ubuntu server “serving a OSM map”? If so which software are using for that?

Do you have a data.osm.pbf file?
It can be edited in JOSM.
Don’t forget to make backups.