Marcus Agrippa died too soon to be a candidate as father of Jesus, but there is no denying that Herod schmoozed Agrippa big time, and so we can't rule out that he might have allowed/offered him the privilege of siring a royal Herodian child. When Agrippa died, Herod had to scramble to maintain his good connections with Rome. Fortunately for him Augustus reconfirmed his standing and according to Josephus also upheld Herod's right to order his succession as he pleased. We might expect Augustus to have dictated succession in Israel if one of his own sons was involved.
Here's a set of Herodian genealogies that are fairly clean:
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