After placing a bounty on this question, I was directed to another question that was awfully similar. Based on a clue from the comments on that question, and a healthy dose of sheer dumb luck, I suspect this is "The Sun and I" by K. J. Parker. It was published in the Summer 2013 edition of Subterranean Press Magazine.
“We could always invent God,” I suggested.
We’d pooled our money. It lay on the table in front of us; forty of those sad, ridiculous little copper coins we used back then, the wartime emergency issue—horrible things, punched out of flattened copper pipe and stamped with tiny stick-men purporting to be the Emperor and various legendary heroes; the worse the quality of the die-sinking became, the more grandiose the subject matter. Forty trachy in those days bought you a quart of pickle-grade domestic red. It meant we had no money for food, but at that precise moment we weren’t hungry. “What do you mean?” Teuta asked.
“I mean,” I said, “we could pretend that God came to us in a dream, urging us to go forth and preach His holy word. Fine,” I added, “it’s still basically just begging, but it’s begging with a hook. You give money to a holy man, he intercedes for your soul, you get something back. Also,” I added, as Accila pursed his lips in that really annoying way, “it helps overcome the credibility issues we always face when we beg. You know, the College accents, the perfect teeth.”
The students do have several "miracles" attributed to them (some through dumb luck, some through careful planning and foreknowledge). However, the scheme begins to unravel when the "made-up" god appears to the protagonist in a dream and asserts His reality:
“You made me up,” he [God] said firmly. “Let’s just think about that. You were trying to find a way to feed yourself and your friends when you were poor and hungry, and an idea came into your head.” He smiled. “Where do you think that idea came from?”
“I made you up.” I couldn’t seem to get him to understand. “I invented you as part of a criminal conspiracy.”
He shrugged again. “You gave me life,” he said.
The protagonist eventually breaks off from the "Orthodox" church and inspires his own schismatic sect.