If they are under your jurisdiction, then they can be drafted into the military and/or be compelled to serve jury duty. Can a foreign national/illegal alien be drafted?, serve on a jury?
Who must register? (See website for complete chart)
Permanent resident aliens
Special (seasonal) agricultural workers (I-688)
Refugee, parolee, and asylee aliens
Undocumented (illegal) aliens
Dual national U.S. citizens
I hope you find this illuminating. Thank you for reminding me of additional evidence that illegal aliens are nevertheless under the jurisdiction of the United States.
As an additional followup on your question, aliens(illegal or not) are not considered “peers” (as in jury of your peers) and hence are not liable for jury duty. But they still are liable for the draft.
I don't want a foreign national or illegal alien on a jury judging me. They all have alien "thought processes" about law and justice.