The Northern Ireland Football League (NIFL) stated that 'Stute defender Anthony Hargan had not been registered in according with League Cup rules.
"The case was considered by the NIFL League Cup Committee today (Wednesday 13 October) and has ruled that the player has not been registered in accordance with Rule 23 of the NIFL League Cup Rules 2021/22," read NIFL's statement.
"Therefore, in accordance with Rule 24 of the NIFL League Cup Rules 2021/22, Institute FC will be dismissed from the competition and the club losing the game in such circumstances (PSNI FC) shall replace the dismissed club and progress to the next round.
"The ineligibility has not impacted the outcome of any Lough 41 Championship matches."
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Brian Donaghey's men become the second team to be dismissed from this season's League Cup.
In September, Larne were thrown out after also having been found to have used an ineligible player in their second-round win over Premier Intermediate side Limavady United.