That is right. If you were not the bio-parent you cannot get the child-related credits like child tax credit or earned income credit for children even if they lived with you and your girlfriend. If a child who was not related to YOU lived with you the whole year you could get the $500 credit for other dependents for claiming them. That's all.
If you were not legally married to their mother they were not your step-children. They were your girlfriend's children who lived with you.
10-27-2020 Edited to clarify----You said you and the children's mother were not married. If you and your GF lived together and you were not the bio-parent you could not get child-related credits for claiming the children except for the $500 credit for other dependents. If you and the children's mother were legally married that would make them your step-children and you would be able to claim them just the same as you could claim biological children.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
