From what I understand, you want to add a custom claim to the access token which is issued to your API to authorize user for the requested resources. To do so, there is a Post Login Flow (Actions feature) with a method: api.accessToken.setCustomClaim(name, value).
Hope this helps, please let us know any questions!
Thank you for your response @marcelina.barycka i want to add the custom claims after the user make a choice in my app (NextJS app the value is the value of the choice)
So i want to change the token from my app goes to Auth0 and returns to my next app with the new token so i can send it to third-part API
The flow is described in this doc - Redirect with Actions (redirect to an external page during the login flow and use the gathered from user data to add custom token claims that will be later returned to your app).