Services have been significantly reduced in many areas due to the spread of Covid-19, but Northern said its aim was to deliver services on key routes for those who cannot work from home.
Last night, Prime Minister Boris Johnson said people should be travelling to work "only where this is absolutely necessary and cannot be done from home."
Norther said: "Everyone at Northern is working to provide the best possible rail service during this difficult time, but it is simply not possible to operate our usual timetable.
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"Where we are not able to run trains we will seek to provide rail replacement road transport.
"Though we continue to run services, the Government is advising that, if possible, people should avoid non-essential public transport use and try to avoid rush hour, varying usual travel times to prevent crowding and if possible, work from home."
Those who are not able to travel – or choose not to travel – during the pandemic are entitled to a refund or partial refund depending on the ticket they hold.
Timetables affected by the changes in Yorkshire include:
York, Leeds and Colne to Preston and Blackpool: (Monday to Saturday)
Sheffield to Adwick and Scunthorpe: (Monday to Saturday).
Hull to Bridlington and Scarborough: (Monday to Saturday).
York to Harrogate to Leeds (Harrogate Line): (Monday to Saturday).
Sheffield to Gainsborough to Lincoln/Cleethorpes: (Monday to Saturday).
Leeds to Nottingham via Castleford: (Monday to Saturday).
York to Selby and Hull and York to Sheffield via Pontefract Baghill: (Monday to Saturday).
York and Selby to Leeds local stopping services: (Monday to Saturday).
Leeds - Goole Flooding.
Leeds - Manchester Victoria / Preston: (Monday to Saturday).
Manchester - Blackburn via Todmorden: (Monday to Saturday).
Ilkley to Leeds and Bradford Forster Square (Wharfedale Line): (Monday to Saturday).
Skipton to Leeds and Bradford Forster Square (Airedale Line)
Leeds and Wakefield to Knottingley and Goole (Pontefract Line)
Leeds to Sheffield and Doncaster (Wakefield Line): (Monday to Saturday).
Huddersfield to Sheffield (Penistone Line): (Monday to Saturday).
Bradford Forster Square to Leeds: (Monday to Saturday).
For full details of Northern’s timetables, check the website.