"Y Path" gets a technical definition from the Office of the Rail Regulator, in terms of track access rights, in a short document I found here -
https://www.orr.gov.uk/sites/default/files/om/Proposed-new-Schedule5-annexB.pdf
As has already been said in previous posts, I think 'Y' paths are typically associated with freight services which run to or from different terminals as required, sharing the same timings over at least part of the route, where only one option can actually run on any particular day.
A good example of a Y path can be found in the Dec 2020 Freight WTT, section WK03, page 11 (click through to the relevant section) -
https://www.networkrail.co.uk/running-the-railway/the-timetable/working-timetable/
On a Friday there are 5 different "Y" path options departing Angerstein Wharf at 11:07 (one of them is an 11:03 departure, but they all pass Charlton at 11:22 and use the same "path" at least as far as Hither Green).
There's a 6V65 to Acton, 6M55 to Wembley, 6Y55 to Woking, 6U55 to Hither Green sidings, or 6M56 to Cricklewood. Only one of these could actually run on any particular day.
Two other examples that spring to mind are the schedules for the potash trains from Boulby. There are typically identical headcodes and departure times for trains to either Tees Dock or Middlesbrough Goods, as required by the customer. Having both schedules in place in the WTT as a "Y option" saves time having to create new schedules for each weekly plan or any amendments to it.
Another Y path that's been in the timetable for years is the evening train from Merehead to either Eastleigh (7O43) or Botley (7O44) Foster Yeoman terminals.
Adding to some of the previous comments:
"Path" is sometimes used loosely and interchangeably with "schedule" although it's not quite the same thing, for example "The signaller says there's no path in the system for 6M55" or "Network Rail are going to put a path in for it" (i.e. create a schedule on their computer systems). Sometimes you might run one train in the path of another train that isn't required. For example there is a regular 6X77 Dagenham - Mossend car train. If this wasn't running on a particular day, you could use this "path" to run a train from Wembley to Warrington Arpley, or Warrington Arpley to Carlisle, for example, using the same timings.
Pathways can refer to potential "slots" for trains, for example if you say something like "there are paths for X number of Class 4 container trains per hour on Y route." Or there might be potential paths for a freight train during most of the day from a terminal on a particular branch line if it departs at 13 minutes past the hour - even though there may be no actual schedules at these times, there is a "path" where it could fit in between other timetabled trains without delaying them.
"No path available" basically means there is no way of creating timings for a train, close to the requested departure and arrival times, without conflicting with other services and delaying them. There could be conflicts at junctions, where one train will have to wait for the other, or delays caused by one train now having to follow a train in front which is slower, stopping at more stations, or where there is just insufficient "headway" between planned trains to add another. "No path available" might be a phrase you hear if you are trying to arrange something "ad hoc" through the "Very Short Term Planning" process (VSTP), such as a freight movement across London during peak hours. As an example where no path would be available, there is a regular loaded spoil train (6E35) from Acton to Peterborough which departs around midnight and runs along the East Coast Main Line via Welwyn. If you wanted to alter the timings and change the departure time to the start of the evening peak, there would almost certainly be "no path" for it - no way of running it without commuter services getting stuck behind it and causing delays.
I think a lot of the local Aire Valley trips would probably have been planned on a weekly basis, with schedules created to suit and not too many conflicts with passenger trains to worry about. The longer distance services in later years (along the Settle & Carlisle or the East Coast) were more likely to have been planned as "Y" options that could serve Drax / Eggborough / Ferrybridge as required, or continue to somewhere like West Burton, from Scotland or the North East (if they weren't staged at Milford Sidings first). In BR days I think a lot of the coal from the North East to the Aire Valley was staged at York yards, so the main line part of the journey might have been in the WTT but not necessarily the colliery / power station trips at each end (possibly there were Y paths from York to the power stations). It would be interesting to know how much power station coal traffic was actually in the WTT in BR days.