I have a new 100A 120v sub panel. When there is no load I get 117v. When I put a load on any one circuit (one 75w bulb) voltage drops to 3 or lower and the light does not go on. Nothing is tripping either

Follow the voltage while light is on starting at first panel lugs, the out of Breaker, then to lugs on second panel, then terminals from circuit breaker to see where it is getting lost.
A loose wire, connection, or breaker not plugged all the way on buss can do this.

This does not make any sense.

You have a 100 amp sub panel, correct? How far are you from the main panel? Are you in the same building as the main panel? If you are in a remote building, did you set up a new EGS?

What is the size of the cable you brought over? Are you using a double pole single throw breaker off your main panel? Did you bring Black, Red and White over from the main panel?

What size breaker are you using for the branch circuit from the sub panel to the load? What size conductor are you using from the breaker to the load. Is it a 14/2 for 15 amp or a 12/2 for 20 amp"?

We need a lot more information from you.

You have a loose connection somewhere like they said above. How many breakers are in your panel box? If more then one go to another outlet in your house and try the same test you did to find out about the 3 volts. If it is the same then it is a problem with the main wires coming into your panel, If it works the way it should it is either a bad breaker on that circuit or a loose connection on that circuit, try tightening the screw where the wi8re enters the breaker, also look at the bar where the breaker connects to the panel.