Some exchanges offer inverted maker/taker fees. The BATS-Y exchange charges $0.0030 for providing liquidity, and pays $0.0020 for removing it. Now consider another situation. BATS-X has 10,000 shares offered at $10, and the BATS-Y book is empty. We’re considering where to send a $10 limit sell order. If we send it to BATS-X, we’ll receive $0.0025. But we’ll only get this if our order is executed, and there will be 10,000 shares ahead of us. If we send our order to BATS-Y, we’ll pay $0.0030, but our order will be at the front of the book. We also know that BATS-Y is a more attractive place to send a market order. Let's say $10 is the NBO, if someone lifts the offer, shouldn't price execution follow price/time priority as in 10,000 shares would be executed first no matter which exchange it is posted at? So even though your offer is first on BATS-Y, shouldn't the buy order go first through the 10,000 as it was posted first?
I do not think that is correct. https://markets.cboe.com/us/equities/membership/fee_schedule/byx/ The $0.0030 is a fee for re-routing to an exchange with liquidity.
Looking at the link from Robert Morse, it appears that CBOE has two inverted and two other non-inverted exchanges. I wonder how retail brokerages sends their auto routing orders to the CBOE exchange in light of this, one imagine the free commission brokerages probably routes only to the fee paying exchange.