Yes you can have our own or you can use the inbuilt one. In Cpanel there is option "Error Pages"
You can use that
Other wise you can create your own and add this to .htaccess file
ErrorDocument 400 /error/400.htm
ErrorDocument 401 /error/401.htm
ErrorDocument 403 /error/403.htm
ErrorDocument 404 /error/404.htm
ErrorDocument 500 /error/500.htm
Provided you placed the error handling web pages in error folder in your public_html