Jus a note, in 2016 Parse has closed (it's now open source and you run it on Heroku or whatever). There are many other "baas" such as Firebase etc.
Since there seems to be some confusion,
(a) your current service has no API. it is, thus, unfortunately essentially useless so your most absolutely time saving step from here would be just scrap it and use parse (or another baas) as the backend. you can have parse up and running in minutes. what previously took server developers man-years is now just like "a consumer product", just make a few clicks to add column-names
(b) your current service has no API. assuming yo DO WANT TO continue to use it, you will have to somehow add an API, using php or whatever. there's no way to avoid this. IF you do that, then you could (if you wanted) make a "basic" API that parse can get the info from, and then use parse to actually connect to the ios/android builds (since that is so easy)
TBC, here's literally how you do that in Parse,
https://parse.com/docs/cloud_code_guide#networking
"Cloud Code allows sending HTTP requests to any HTTP Server" it's that simple.
As I mention above, it's far easier just to scratch your current backend and change to a bAAs (such as Parse). you have to "go with the times" you know?
Note that the development and testing of an API on a service is incedibly time consuming, it is a huge job for a team.
Here on this question you seem to be asking about bAAs and how they fit in the formula. the answers are:
(1) if you simply scrap your current service, do everything on a baas: it is trivial. what used to take literally man-years is now a few clicks
(2) in terms of "helping you ADD AN API to that service". bAAs cannot help you with that in any way and is irrelevant
(3) if you DO have a service with an API, yes it is relatively easy to have bAAs "link in" to that. (i include literally the doco from pare on doing that above)
Hope it helps!!!
