We performed deep observations to search for radio pulsations in the directions of 375 unassociated Fermi Large Area Telescope (LAT) gamma-ray sources using the Giant Metrewave Radio Telescope (GMRT) at 322 and 607 MHz. In this paper we report the discovery of three millisecond pulsars (MSPs), PSR J0248+4230, PSR J1207$-$5050 and PSR J1536$-$4948. We conducted follow up timing observations for around 5 years with the GMRT and derived phase coherent timing models for these MSPs. PSR J0248$+$4230 and J1207$-$5050 are isolated MSPs having periodicities of 2.60 ms and 4.84 ms. PSR J1536-4948 is a 3.07 ms pulsar in a binary system with orbital period of around 62 days about a companion of minimum mass 0.32 solar mass. We also present multi-frequency pulse profiles of these MSPs from the GMRT observations. PSR J1536-4948 is an MSP with an extremely wide pulse profile having multiple components. Using the radio timing ephemeris we subsequently detected gamma-ray pulsations from these three MSPs, confirming them as the sources powering the gamma-ray emission. For PSR J1536-4948 we performed combined radio-gamma-ray timing using around 11.6 years of gamma-ray pulse times of arrivals (TOAs) along with the radio TOAs. PSR J1536-4948 also shows evidence for pulsed gamma-ray emission out to above 25 GeV, confirming earlier associations of this MSP with a >10 GeV point source. The multi-wavelength pulse profiles of all three MSPs offer challenges to models of radio and gamma-ray emission in pulsar magnetospheres.
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