The "SS" is a standard part of a the notarization language on a document which is known as the "jurat" of a document.
The “SS” stands for the Latin term “scilicet” which means "in particular" or "namely" and simply indicates that the place where the document was signed is described in the preceding bracketed portion of the jurat.
You do not have mark anything or fill in any additional information on the “SS” designation itself. Completing the areas marked "State of ________" and "County of _________" with the location where the notarization takes place is where you enter the necessary information for the venue portion of this form.
You are no doubt confused because one of the possible jurats for the form (the one for an individual petitioner) has a fill in the blank line which I have screen shotted below:
The inclusion of a line to fill in following "ss." on the form is a drafting error in the form, which is not repeated in the other jurats on the form, probably because the person who drafted the form didn't know what it meant.
Another Flaw In The Form
The same portion of the form also has another drafting error although a less innocent one and it appears in all of the jurats on that form.
It should have omitted the words "New York" because it is not mandatory to actually notarize the Petition at a location that is physically within the State of New York, even though usually this is what will be done. On the other hand there was a requirement to sign the document in New York State, in contrast (which there isn't) then the fill in the blank line following "New York" should have been omitted.
This is a case of someone gratuitously including an apparent extra-statutory requirement in a form (probably because they often have to reject forms if the state isn't filled in at all), without an explanation that "New York" may be crossed out and replaced with another state in the space following the name of the state.