It's possible that a new, combined antagonist could emerge. Maybe a wizard who has been influenced by the darker aspects of both worlds. He could have learned some of the combat and sneaky tactics from Ziva's world and combined them with dark magic. This character could be jealous of Harry's unique heritage and want to take it for himself, believing that he could use it to rule both the wizarding world and the world related to Ziva David.
The main antagonists could still be the Death Eaters. Since they are the traditional enemies in the Harry Potter universe. They would see Harry, even as the son of Ziva David, as a threat to their dark plans. They might target him not only because of his connection to Harry Potter but also because they fear the unknown elements that Ziva's heritage could bring into the fight against them.
Another possible antagonist could be some sort of organization from Ziva's world that doesn't want the two worlds to mix. They might see Harry as a symbol of that unwanted mixing and try to stop him from using his magic in their world or from bringing any magical elements into their normal, non - magical operations. They could be a shadowy group that has been keeping an eye on Ziva's family for generations and now see Harry as a new problem to deal with.
It could be a combination of Voldemort and one of Ziva's enemies from her own world. Imagine if Voldemort made a deal with an enemy of Ziva's, like a powerful terrorist or a corrupt politician. They would team up to try and take over both the magical world and Ziva's world.
One possible plot could be that Harry discovers his true mother is Ziva David through some magical means. Maybe a powerful spell reveals his hidden heritage. He then has to deal with the fact that he has a connection to two very different worlds - the wizarding world of Harry Potter and the world of Ziva David, which might be something like the world of NCIS in the original show. He could struggle to balance the two identities and the different skills and knowledge from each world.
Obviously, Harry Potter and Ziva David are main characters. Harry, with his knowledge of the wizarding world, and Ziva, with her worldly and combat - trained skills. Their interactions would be the core of the story, whether they are friends or rivals.
The Death Eaters would be obvious antagonists as they are in the original Harry Potter series. But also, there could be a group of shadowy figures from Nightwing's world who oppose the idea of a wizard - Nightwing hybrid. They see Harry as an abomination and try to eliminate him before he can fully realize his powers.
There could also be some characters from the Doctor's universe who oppose the idea of a half - wizard, half - Time Lord. They might come to the wizarding world to try and stop Harry from using his combined powers, fearing it could disrupt the balance between the two universes.
It could be some dark wizards who are threatened by Harry's unique heritage. They might see him as a potential threat to their power and plans. Maybe they want to use his connection to Spike for their own evil purposes and when Harry refuses, they become his enemies.
Voldemort could still be a main antagonist. His dark magic and thirst for power would put him at odds with Harry, especially if he sees Harry's connection to Black Widow as a threat. Another could be some of the more traditionalist wizards who don't trust Harry because of his strange heritage.
The Death Eaters could still be the main antagonists. Even though Harry has this new connection to Lady Magic, the Death Eaters, loyal to Voldemort, would see him as a major threat to their dark plans and would continue to try to kill him.
It could be another magical creature or group that is jealous of the power that the vixen holds and by extension, Harry as her adopted son. Maybe there is a group of dark wizards who want to harness the vixen's magic through Harry, and they become the antagonists as they try to capture him.
The Ministry of Magic could be the main antagonists. Since Harry is the abandoned son of Artemis, they might see him as a threat to the stability of the wizarding world. They could try to suppress his powers and keep his identity a secret.