I have created custom quick action buttons on lead object and on a custom object. I have set visibility for each quick action button, but the filter is reflecting in the experience site object pages. Dynamic actions have been enabled.

Hey @Mohit Edupuganti, i would recommend creating a separate page layout (not lightning page) for experience site users and make sure you don't add any action buttons there. Assign this page layout to the site user profile. 

This way it will keep the UI separate for internal and external users