How do I recreate this halftone gradient border?

(I’m pretty sure your example isn’t a halftone but a texture over a gradient that looks a bit like a halftone; the image quality isn’t great though and if you need this for screen printing then you do need a halftone…)

The following steps are essentially exactly the same in Illustrator & Photoshop.

Create your inner shadow as you normally would (it doesn’t really matter how; I used an Inner Glow effect set to black with no blending). Importantly though, use a single ink color (i.e. for black, use 100k), otherwise you’ll get a different halftone screen for each ink.

Effect → Pixelate → Color Halftone…