Hi @Deepak Trivedi ,
In SharePoint 2013 or later, there is a new permission level Remote Interfaces Permission that in particular prevents anonymous users from accessing CSOM libraries.
To enable CSOM for Anonymous Users, please do like this:
Go to Central Administration
Go to Manage Web Application
Select your Web App
Click on Authentication Providers in the ribbon
Click zone "Default".
Uncheck "Require Use Remote Interfaces Permission"
Then in Site Permissions, set like this:
Then tested with this Jsom ECMA Script:
It's working to add items with anomymous access:
Reference: