is it mandatory to use export patch for changing object?

Another option to export patch would be to create a new application, add the object you modified to that application, and export that application. When you deploy that application to a higher environment it will update the modified object.

My preferred method for this when creating small hotfixes to push to Production is, prepare the hotfix in its own new (small) app package in the hotfix environment, then add the contents of that application to a patch, and import the patch into a dedicated patches / hotfixes app package in the target environment. This allows us to keep track of recently changed objects if necessary, without cluttering the production environment with zillions of individual patch apps.

My preferred method for this when creating small hotfixes to push to Production is, prepare the hotfix in its own new (small) app package in the hotfix environment, then add the contents of that application to a patch, and import the patch into a dedicated patches / hotfixes app package in the target environment. This allows us to keep track of recently changed objects if necessary, without cluttering the production environment with zillions of individual patch apps.