No, you can't sue for your lost wages, your time spent preparing your defense, or your stress.
You could report the citing officer to their supervisor, and/or pressure your elected official to change the alws that give immunity to law enforcement officials who perform their duties negligently.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls --- we need an actual agreement confirmed in writing before any attorney-client relationship is formed. Please don't expect me to respond to your follow-up queries. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
In California you could not and I expect that is the same in NY. It is a criminal summons and you have to heed it. Further, despite your friend's theory, you need to show up and make your defense. You can vent your outrage then and your theory why this is brought against you but appear you must and you cannot collect wages for doing so.
Contact your local bar association for referral to an attorney who specializes in this. Often, but not always, the attorney will do an initial consultation free of charge. You will then be in a better position to determine what to do next. Best of luck to you!
If you liked this answer, click on the thumbs up! Thanks. Eliz. C. A. Johnson Post Office Box 8 Danville, California 94526-0008 Legal disclaimer: I do not practice law in any state but California. As such, any responses to posted inquiries, such as the one above, are limited to a general understanding of law in California and not to any other jurisdiction. In addition, no response to any posted inquiry should be deemed to constitute legal advice, nor to constitute the existence of an attorney/client or other contractual or fiduciary relationship, inasmuch as legal advice can only be provided in circumstances in which the attorney is able to ask questions of the person seeking legal advice and to thus gather appropriate information.