Yonkers??? This is a long shot but not a real long shot.
Francis Mesnard Bancker bp: April 8, 1765 served in the Revolutionary War.He was named after his paternal grandfather.The Mesnards were an old NYC Huguenot family.Mine moved to Greenwich CT.Their child died in an accident in Yonkers.I spent many years looking for who could have been living in Yonkers that they would visit.I figured out it must have been the Banckers.Oh by the way, if you do discover FMB was your ancestor I can send you a picture of his mother.She was painted by a brother in law, Kilburn.The most sought after portrait painter in NYC.I got a snap shot from the Aycrigg family.They all descended from this line and own the painting which is quite valuable.The Met only owns 1 Kilborn.
Francis is the French form of Frank.That form of the name would imply a French connection.Just now, I did some checking, I have a good deal of Bancker 'trees'.I collected them while trying to find some living descendents.I bet you are it, because there are noFrancis Bankers not descended from John and Altje.These people were very 'proper' they used family names.The Aycriggs are still recyling 18th century names today.
The hard work will be to trace back.Check the DRC records you might get lucky.They may still have been members in 1812.
I guess this would be in order since he could very well be your ancestor. Francis Mesnard BANCKER, bp. Apr 8, 1765. Ulster Co, NY, Priv, Apr 30, 1782, -Jan 1, 1783, Capt John L. Hardenberg's Co, Lt Col Frederick Weissenfel's Rgt of Levies, Land Bounty Right of 200 acres. Patriot.
If not, his dad Johannes/John was a patriot as well.It is likely you descend from him.