There are several parts in your problem.
1° you want to go to college outside of Texas: have you explored colleges? Which ones do you like (beside Fordham): in particular, do you want to attend a Catholic university specifically?
2° you want to go to NYC : why NYC specifically?
3° you need your parents onboard : what is their reasoning?
4° your parents want you to stay in Texas: will they pay for Texas public universities? Texas private universities?
Is it more important to you to go to NYC (even if much later) or go to college outside of Texas (after HS)?
NYC : you cannot attend Fordham or another NYC university until you’re 24. Until then, you’re a dependent of your parents for college financial aid/FAFSA purpose.
Leave Texas: this will depend on your stats and on whether your parents would be okay with another state that is not Texas.
What’s your class rank? Your GPA? What core classes did you take this year and are you scheduled to take next year (ie., English, Math, Foreign Language, Science, Social Science)? Did you take the ACT (or SAT)?
In all cases you should apply to the Texas uni