no worries its honestly pretty vague since they don't really interact on screen!

the tldr of it is that they have no blood relation, but as someone whose capable of developing soft spots, he's developed somewhat of a sense of responsibility over them and acts as a psuedo-guardian.

gatekeeper & priest (hitsugi/negi's father) both have ties towards godfather, and gatekeeper holds a sense of responsibility towards godfather that includes cleaning up the mess that priest has made. as victims of priest, hitsugi and negi sort of fall beneath that. he's mostly hands-off with them, but appears to help them stay afloat and find what they need to be independent. in turn, hitsugi and negi have developed a fondness back towards gatekeeper and call him "ojisan", "uncle".

right now we know that...

• it was likely gatekeeper who secretly informed hitsugi where priest kept his older sister
• supplied hitsugi/negi IDs so they can live wherever they like around the world
• aided negi in a plan to rid of priest so they can live without their lives in danger
• took them in under his wing afterwards for the period of time they won't be able to safely show themselves in public

maybe more! but these are the ones i know best
these actions, while they help aid hitsugi and negi, also fall under gatekeeper's attempts to undermine priests power (such as informing hitsugi of his older sister's existence)