If you have client-side JavaScript executing REST calls, it will always run in the context of the current user, which means you cannot do anything in a REST call that the current user does not have permission to do themselves.
If you are using an on-premises installation of SharePoint Server that is using integrated NTLM security (meaning your Active Directory users are usually automatically logged into SharePoint without entering their credentials), then when your code attempts a client-side REST call that attempts to perform an action that the current user is not authorized for, the browser will automatically prompt them for AD credentials for a user account that Does have access.
If you are using an Online environment or one without integrated security, then instead of re-prompting the users for credentials, your code will just receive a 401 Unauthorized.
If your SharePoint farm is using integrated security with your local domain, there is no way to directly stop the user from being prompted for credentials when you try to access a resource they do not have access to. Instead, you will need to use the REST API to see if the current user has permission to perform the action, and display a more friendly error if they do not.
The following is an example, borrowed from a previous stack exchange post on checking a user's permissions:
function checkPermissions() {
var call = jQuery.ajax({
url: _spPageContextInfo.webAbsoluteUrl +
"/_api/Web/effectiveBasePermissions",
type: "GET",
dataType: "json",
headers: {
Accept: "application/json;odata=verbose"
}
});
call.done(function (data, textStatus, jqXHR) {
var manageListsPerms = new SP.BasePermissions();
manageListsPerms.initPropertiesFromJson(data.d.EffectiveBasePermissions);
var manageLists = manageListsPerms.has(SP.PermissionKind.manageLists);
var message = jQuery("#message");
message.text("Manage Lists: " + manageLists);
});
}
sharepoint-onlineandsharepoint-server, are you using SharePoint Online in O365, or are you using a specific on-premises installation of SharePoint Server? – willman Mar 04 '20 at 13:53