Confusion regarding a library of Digital Signal Controller I'll be using a NXP DSC with 56800Ex core and my aim is to implement a Elliptic IIR Filter in it.  

The User Reference Manual of the 'General Digital Filters Library' (which is available here) has functions to implement IIR Filters. 


  


But on page 3-19 shown above, it says 


  The filter coefficients are calculated using Butterworth approximation.



Does this mean that we can only use Butterworth Filter? Also, as per my knowledge, we have to give the coefficients and therefore other filters can also be implemented. 
So what exactly does the function do? 
Can I implement a Elliptic filter using this function or not? If not, then what should I do use Elliptic filter?
The function you are refering to only implements an order-1 filter. There is another function for order-2 filter.

If you want to implement an order-3 filter, you will have to split it in an order-1 filter and an order-2 filter. There are many ways to do it, but cascading the filters, as we would do in the analog world, is a good solution, albeit not optimal IIRC.

As to your original question, since the function refers to an order-1 IIR filter, an order-1 Elliptic or Butterworth, will have the same coefficients if you design them with the same cut-off frequency.

However, starting with order 2 or more, the coefficients will not be the same.