2008 Sante Fe .. I have to jiggle the battery connector to get the car to start. The alternator and battery was replaced less than 3 months ago! What could be the problem?

You answered you own question actually. If you have to wiggle, jiggle, the cable terminal it's not tight. If it has corrosion baking soda and water will clean it, but still. wear latex gloves and remove the cable, clean as well as possible with a wire brush on cable and battery post, and re-install and tighten...you may have to buy a new nut and bolt. but it should not move whatsoever. If side post battery, pretty much the same, then put vaseline on the terminals to prevent corrosion.and this applies to both cables, the red Pos+ and black Neg- if it's not getting a ground, same problem

LOL.. I will definitely clean and tighten the terminal. I will tell you how it goes.... Thank you so much for your quick reply.

Either your battery terminals are going bad, or the battery they put in has narrower terminal posts than the previous one. In many imports they install lead battery post shims so that the battery terminals connect to the battery terminal posts better and not remain loose. They cost about $3-4 USD each and you can easily install them yourself with only a few tools in under 15 minutes each terminal.

Yes, you need a good connection. Mine was not starting. I found that the ground wire coming from the negative battery tierminal to the chassis was loose at the chassis. Wiggling it caused the lights to come on and off. I removed and cleaned both ends, then replaced. Has started with no issues for a week now... about 40 times.

Then you were lucky indeed buddy. Always start with the simplest and work up from there. When it gets to the point that its an electronic and not electrical issue, then you need some serious help.