If I am dating an ex-felon (non-violent drug charge), could it jeopardize custody of my daughter?

There are some factors here you can consider. First, if the guy you are dating does not have a history of multiple drug charges and he has successfully completed whatever drug testing/counseling programs that were part of his original sentence, that would be a good thing. Second, does he have any history of domestic violence or any FAPA restraining orders arising from prior relationships? If not, that's a good thing. If he does have such a history, you need to know about it anyway if you are getting into a serious relationship. If your new friend has done what he had to do to get past the conviction and he has no history of domestic violence or harassment, then your ex would be wasting his time to try to terminate your custody. The rule is that he has to prove that there has been a material change in circumstances in order to change custody in which case he would have to prove that there is a significant threat of harm to your daughter if the guy stays in your life. On the other hand, if you have a joint custody order, you should talk to a lawyer and tell him or her how you managed to agree to that in the first place. In Oregon, the normal custody order is for sole custody to one parent with the other parent getting some amount of parenting time plus an obligation to pay child support.