“United States
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In the United States a private person may arrest another without a warrant, for a crime occurring in their presence. For which crimes this is permitted may vary state by state.[77]
Common law
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Most states have codified the common law rule that a warrantless arrest may be made by a private person for a felony...”
https://en.m.wikipedia.org/wiki/Citizen’s_arrest
Crossing the border is not a felony, it is a misdemeanor.
A key part of that is “a crime occurring in their presence”. Unless a militia member actually saw someone cross the border how would they know that someone is here illegally?