The latter is correct: "the city and its residents" ..... Note that I didn't use a capital letter or a period, since it's (it is) not a full sentence, but rather a sentence fragment (unless you intend to use it as a heading or title of something, in which case you would capitalize all the words).
Besides the misuse of "your/you're" it seems "it's" is the most common error you'll find in today's written English.
I think the reason for the common mistake is because we were taught about using an apostrophe with "possessives" ... like "Megan's bike" (the bike belonging to Megan) .... or .... "the city's residents" (the residents belonging to the city.)
"the kitchen with it's new appliances" (incorrect) DOES suggest "the appliances belonging to the kitchen"
It would seem this "possessive" logic would carry over to "its" with an added apostrophe, but it's not the case...
I use these rules when writing:
Use "it's" ONLY when you want to communicate "it is" (It's a sunny day.) (Tell me when it's ready.)
Otherwise, use "its."
Similarly, use "you're" ONLY when you want to communicate "you are" .... or "they are" (they're).
Otherwise, use "your" or "there" or "their."
With the apostrophe included, your first example reads "the city and it is residents" which we all agree is incorrect. :)