The 16-year-old is nine under as he looks to keep the English Men’s Open Amateur Stroke Play title in Yorkshire hands following the victory by Wath's Nick Poppleton last year.
First-round leader Charlie Strickland (Ham Manor) scrambled his way to 70 and stayed in touch in second place. A further shot back and sharing third place on five under are England’s David Langley and Jake Hapgood of Wales.
Schmidt’s bogey free round of seven under is his lowest score in competition and he said: “It all came together, right from the first tee shot.”
That set up the first of three consecutive birdies, which were followed by two more before the turn.
“Then it was just about not making mistakes on the back nine. I hit good tee shots and iron shots, kept the ball in play and holed a few putts when you don’t expect it. That’s when you get a good score,” he added.
As for leading the Brabazon on his first appearance in the championship, the England Boys’ squad member commented: “It’s nice, but I’ve got to go away and try not to think about it. My first goal was to make the cut, because this is a big men’s event, and I’ve done that quite easily, which is good.
“Now I’ve got the weekend and two more rounds, so I’ve got to restart, not think about leading, but just do what I’ve been doing for the past two days and play good golf.”
Fulford's Charlie Thornton is tied for fifth place, five back of Schmidt, after adding a 67 to his opening 71.
He carded three birdies and an eagle at the 591-yard par-5 eighth, but must be sick of the sight of the final hole, which he double bogeyed on Thursday and where he dropped a further shot on Friday.
Wike Ridge's Ben Firth is a shot back of Thornton in a share of seventh spot. He went round in five-under-par 66 having started the day two over.
He had three birdies in his round and two eagles, opening his back nine with a three at the 528-yard par-5 10th and then adding an eagle two on the penultimate hole, a 435-yard par-4.