From the shape of the fruit and what seem to be pinnately compound leaves, what you have MAY be a member of the walnut family (Juglans) of which there are a number of species; http://dept.ca.uky.edu/PLS320/Lecture4juglandaceae.pdf. Do not attempt to consume the fruit until you have someone give you an on-site definitive identification. Here is a fact sheet on black walnuts (Juglans nigra)  for which New York State is near the northern limit of its range: 
http://www.forestry.ok.gov/Websites/forestry/Images/trees,blackwalnut.pdf. Several identification keys mention the fruit (and leaves) having a "lemony" smell, about as close as I could come to "smells like soap." 

Thank you so much for this information! I am very happy that you were able to answer my question. To add I'd like to show you a shocking photo of the fruit cut open. Thank you again and have a nice day!

You're very welcome. And the cut-up fruit does suggest a very green walnut. If you like nuts, it might be worth having someone locally look at your tree to confirm it is walnut.