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Let suppose you are at +3 degrees latitude (3 degrees north of Equator ... for example at Cali in Colombia). At what periods of the year will the sun be at your vertical (at your zenith) at noon?

I know that at Sun is at equator zenith on 21st March and 21st September (spring and fall equinox). So at +3 degree north of equator will it be before or after 21st march? And before or after 21st September?

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The Sun will be at your zenith a few days after 21st March, after it crosses the equator heading northwards* going towards summer, and a few days before 21st September, before it crosses the equator heading southwards* after summer has ended.

* from an Earth-centric viewpoint. We know, of course, that the Earth is rotating about its axis and revolving about the Sun, and that Earth's axial tilt is what causes the seasons and the apparent motion of the Sun across the sky both through the day and through the seasons.

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