Bicycle Mechanics - tire cut

I've been commuting about 12 months on new 700x28 road bike slicks. Got a puncture the other day and there is a cut about 3/16" long right through. I put in a new tube and sealed the hole with some silicone after I inflated it. Do you think the tire should be replaced? Can I get a patch to put on the inside of the tire?

If the casing has been damaged, replace the tire. If it's just the tread, go ahead and ride it.

cut tires can be repaid for emergency return trips but it sounds like you should replace the tire. I think folks say to put the new tire on the back wheel if replacing just one

It depends on what you're doing. I have a bad sidewall cut, and I continue to ride it. Of course, I moved the tire to the rear. I don't want a front blowout. I made a boot with Gorilla Tape and inflated it to 130 psi and rode it, as a test. It's been holding for months. I watch it to make sure it's not progressing.

If you can't afford a blowout, then replace the tire.

But be sure this is your rear tire.

I use 1/32" gasket material and superglue to the inside of the tire. I have found that putting duct taper over the patch keeps the rough edges of the patch from fretting though the tube. Make sure the gasket material is used in piping and is reinforced.
I usually run a booted tire on the rear.
Always put a new tire on the front and move the old one o the rear.

I agree with the carcass patchers. Put some kind of patch inside the tire, a tube patch is adequate. This prevents the tube from bulging through the patch
and protects against the occasional rock that hits the patch just right. I have never had a cut in the tread part to propagate, the tread seems to prevent
that. Sidewall cuts between 6 and 9mm are risky for bulging and herniation of the tube through the cut. 3/16" is too small to toss the tire.