Dads are great for things like contributing the sperm for a baby, telling "jokes" that elicit more groans than laughs, and wearing tall socks with sandals. But as far as smarts go, your mom did most of the genetic work. So don't worry -- those lame dad jokes aren't genetic.
Years of research rounded up by Psychology Spot confirms that most of your intelligence is attached to the X chromosome, and while females get one of those from the father, intelligence genes aren't activated when they're passed down by a male. Sort of a genetic "thanks, but no thanks" situation, with the upshot being that your mom is largely responsible for what a smart young man/woman you've turned out to be! Or what a giant idiot you are.
Now, if you remember your Intersectional Studies 101 class, you know that biology isn't destiny, which Psychology Spot points out: genes are responsible for about 40%-60% of your intelligence, with the rest attributed to environmental factors. If your dad's a bumbling idiot who watched daytime television with you as a child, any genetic intelligence won't be put to full use; the flip side of the coin is true for if he's a brilliant mathematician who bounces solutions for Hilbert's problems off you, though the former sounds a lot more relaxing.