Yours is not necessarily a lost cause. How long ago were you convicted? Did you complete everything the court required? Did you go through drug treatment? Are you still involved with relapse prevention, like NA? Many people have bad stuff in their history. It's what you do about it that counts. If it has been a long time and you can show that you really have dealt with it, then you have a chance. But you are talking about parenting a tiny baby.
You didn't say how old your other child is or how often you see her. Many people say they have joint custody but that doesn't mean that they see their child very often or are really involved in the kid's life. If you don't see this child often or she's a teenager, you would be really smart to take a parenting class. A big reason men often get excluded when it comes to newborns is that moms are usually very worried about the child being properly cared for and being safe. Doing a parenting class can help a lot with the mom and the court.
Unless the mother has issues herself, she would likely get full custody. But that doesn't mean you shouldn't do everything possible to make sure you get maximum time with the child. Showing that you have dealt with your drug history and that you are current on parenting little babies will help make the mom and the court comfortable with you having lots of visitation. Doing nothing will result in you getting nothing.
In most states the test for custody is what is in the "best interest of the minor child". The fact that you have a prior criminal conviction (if you do) for growing marijuana is not a good thing. However, in most states it would be only one factor in your case and should not be the controlling factor if you have turned your life around and there is no current evidence you are involved in illegal activity.
It is critical you consult with a local lawyer in your town to ask them the laws where you live as that will be the best advise. Best of luck.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.