OpenMRS has set of Mobile clients which consumes OpenMRS core data via REST web services module.
The ideal candidate of this 'Task' has to be familiar with iOS developments, Objective C language, REST Web services.
Note: The intension of this Task isn't to develop a fully functional client like in Android. But at-least to have some basic functionality with limited features. i.e: Login, MainMenu (with the completed ones.), Find Patients.
Please see the OpenMRS Android client for a similar use case: