The RMT union said workers are "solidly supporting" more industrial action as they walked out for the 42nd time since the row flared.
RMT general-secretary Mick Cash said: "I want to pay tribute again to RMT members across Northern Rail on this 42nd day of strike action.
"It is the sheer guts and resilience of our members over the past two years that has kept the fight for safe and accessible rail travel for all across the Northern franchise in the spotlight while the company continue to duck and dive and refuse to face up to the key issues.
"While this basket-case, German-owned company lurch from crisis to crisis, it has only been the determination of RMT members and our supporters from the travelling public, whose solidarity has been instrumental in keeping the focus of the dispute on the campaign for a guaranteed second person on the train with the full suite of safety competencies.
"We thank the public for their continuing support and understanding in a dispute which is about putting rail safety before private profit."
Northern has called for an independent inquiry into the dispute in a bid to break the deadlock.
Managing director David Brown said: "More than 50 per cent of all rail journeys in the UK are made on driver-controlled trains and recently the Department for Transport and Transport for the North publicly confirmed that a second person - in addition to the driver - would be retained on Northern services.
"This second person will provide customer service, including meeting customer needs on accessibility, safety, security, ticketing and information.
"Therefore, there is no reason for the RMT to continue its disruptive and economically damaging strikes, but despite this the RMT continues with its strike action."
RMT members on Northern will strike on every Saturday in January.