I feel like if/when get a "Damian calling for Dad/Baba" in canon, it always has to be super intense, so I'm going throw in an idea I've had for a while:
The Justice League, as well as many other heroes are being mind controlled. Think Maxwell Lord on some alien drugs or Bane juice or both, which would require some real power to defeat. They are in Metropolis because of course there are. Batfam had all been uninvited for whatever reason, needed for potential backup, not told, had another mission, etc.
Batfam realizes that their friends are currently being forced to terrorize the city and they all gather and move into the city to try and handle it (and I do mean every Bat except Batman, including the older ones who aren't technically Bruce's kids).
Damian is told by Dick and Kate to stay up on rooftops as "surveillance" (they don't want him hurt) because the Bats are fighting multiple of their friends and allies, they end up spread out as Damian tries to provide any help he can over coms and try to figure out how to jump into battle without making one of his family members freak out. That is when the Brainwashed Justice League arrives on a rooftop, maybe the one Damian is on, Maybe one he is in line of sight of.
Damian realizes what happened and he, for the first time, feels his age. He freezes. He's actually terrified for a brief moment. He gives off a warning to his family before he actually tries to fight.
Most of the Justice League disperses, leaving maybe 2 or 3 people on the roof with Damian (not Bruce, he went down already). They easily subdue him, taking his sword, grappling hook, most if not all his gear is taken or broken as he fights. He's subdued after a few moments of struggle and brought to the edge of the roof.
Damian is thrown off of a 10+ story building, and he thinks he's going to die, because either no one is near him or they are being pinned down by their brainwashed friends. So he calls out, and his concussed mind can only think about the amount of times Bruce has caught the other Bats.
"BABA!!"
The shriek is heard all around, and through their coms, and the Bats know something is seriously wrong. Damian rarely if ever calls Bruce anything other than Father. It terrifies them even more as they all try to look for him, only to see him falling or hear someone yell that he's falling, bloodied and without gadgets, off of a large building.
It's almost just as scary when they hear Bruce's wail, pained, sorrowful, like he's ripping a part of his body off. Then they hear a grapple and a soft thud from Damian's com. Bruce catches him.
Bruce then, over his own com, explains how to fix everyone (scare them out of it, electric shocks, Kryptonite dummy rounds, etc). Bruce doesn't let go of Damian (bonus if Damian either doesn't or can't fight it because of his injuries). They get everyone back to the Watchtower or Hall of Justice, Bats helping everyone and going over what they need to do to not have this happen again. Then comes the question that seemingly everyone wants to know the answer to.
"Uh... Batman?" It's Superman, seemingly the only JL member that has the gall to ask "Why did Robin call for you like that?" Because no one knows the Bat's are related, no one knows that Bruce is their Dad, mentor, and inspiration.
Bruce is still holding and now bandaged Damian, who's just about to falling asleep in his Father's arms as he hears the almost soft reply.
"I come when any of my family calls. Period."










