The point where the Sun is straight overhead is called the sub-solar point. Its latitude equals the Sun's declination, the Sun's angle north or south of the celestial equator. Its longitude is where it is local solar noon at that moment.
Earth turns once a day, so the sub-solar point races west at about 1,670 km/h near the equator, tracing a line along one latitude. The declination itself changes slowly, by up to 0.4° a day near the equinoxes and almost not at all near the solstices, so the daily lines stack up into a coil between the Tropic of Cancer (about 23.44° N) and the Tropic of Capricorn (about 23.44° S).
A place has a Zero Shadow Day (शून्य छाया दिवस) when this line passes over it. At that moment, local solar noon, a vertical pole casts no shadow. In India this happens between early April and early September: first in the far south, reaching the Tropic of Cancer near the June solstice, then back south.
Positions use the NOAA solar formulas (about 1 arc-minute; times within a minute). The Indian places are city centres; across a city the time changes by about 4 minutes for every degree of longitude. Everything is calculated in your browser.