Adjacent drip edge pieces should be lapped minimum 2 inches. Asphalt shingles should overhang the exterior edge of the drip edge by ¼ to ¾-inch.
Does drip edge overlap gutter?
The face of the drip edge should be overlapping the gutter so that no water is going in between the gutter and fascia and possibly rotting out the fascia that's holding the gutter up.
Should there be a gap between drip edge and fascia?
The best installation method is to leave a gap between the drip edge and the fascia board, about the width of a finger. The shingles should also overhang the drip edge 3⁄8 to 1/2 an inch.