@Granville Rex , Based on your explanation, it looks like your application is a multi-tenant app, that is hosted in your tenant but can be used in other tenants too. In this case, since you would be doing the app registration, that would create the application object and service principal object both in your home tenant, hence you would need to have an AAD Premium License (AAD P1/P2) for your tenant.
But, when another user from another tenant tries to access your application, in his tenant, just the service principal of your application gets registered, and for that no license is required.
Hope this helps.
Do let us know if this helps and if there are any more queries around this, please do let us know so that we can help you further. Also, please do not forget to accept the response as Answer; if the above response helped in answering your query.