How to restrict the email notification/usage to "Verification" and "Forgot Password" function?

Question

Nothing more to add other than the title.

I want the email function on my forum to only send emails when a new user registers (for verification) or when someone wants to reset their password.

I have a limited SMTP relay plan, and I dont want it to get exhausted in a day. Any help is much appreciated.

PS: I searched a lot here in the forum if this question has been asked before, but, no luck.

Comments

Just a pointer at where to look at or whether its possible or not is enough.