Bear with me, this is my own maths/understanding of the below and may be wrong.
https://documents.uefa.com/r/Regulations-of-the-UEFA-Champions-League-2025/26/Article-30-Player-eligibility-Online
Definitions as per uefa.com :
Locally trained player - is either a "club-trained player" or an "association-trained player".
Association-trained player - An "association-trained player" is a player who, between the ages of 15 (or the start of the season during which the player turns 15) and 21 (or the end of the season during which the player turns 21), and irrespective of the player's nationality and age, has been registered with a club or with other clubs affiliated to the same association as that of the player's current club for a period, continuous or not, of three entire seasons (i.e. a period starting with the first official match of the relevant domestic championship and ending with the last official match of that relevant domestic championship) or of 36 months.
Club trained player - is a player who, between the ages of 15 (or the start of the season during which the player turns 15) and 21 (or the end of the season during which the player turns 21), and irrespective of the player's nationality and age, has been registered with the player's current club for a period, continuous or not, of three entire seasons (i.e. a period starting with the first official match of the relevant domestic championship and ending with the last official match of that relevant domestic championship) or of 36 months.
My shorthand interpretation of the above :
Association trained player is someone trained somewhere within the FA's jurisdiction for 3 years between the ages of 15 and 21 (quantity of loans/abroad can mess this up).
Club trained player is someone who has trained at the club for 3 years between the ages of 15 and 21 (quantity of loans/abroad can mess this up).
Locally trained player is someone who fits either of the above rules.
List A as per uefa.com article 31 :
Max 25 players, of which 8 are reserved exclusively for locally trained players. No more than 4 of the locally trained players can be association trained.
List A must specify the players who qualify as being "locally trained", as well as whether they are "club-trained" or "association-trained".
If a club has fewer than eight locally trained players on its List A, the maximum number of players that can be registered on this list is reduced accordingly.
List B as per uefa.com article 31 :
Unlimited in number
A player may be registered on List B if he is born on or after 1 January 2004 and has, since his 15th birthday, been eligible to play for the club concerned for any uninterrupted period of two years, or a total of three consecutive years with a maximum of one loan period to a club from the same association for a period not longer than one year. Players aged 16 may be registered on List B if they have been registered with the participating club for the previous two years without interruption.
31.13
Goalkeepers special rules as per uefa.com article 31 : Each club must include at least two goalkeepers on List A and at least three in total (List A and List B combined).
My shorthand understanding of all the above
You submit 2 lists, A and B. You can field any players registered from either list. In theory if you have enough young players your squad could be unlimited in size.
In List A, you get 17 spots that you can give to absolutely anyone, regardless of nationality, when you signed them etc.
In List A, you can register up to 4 extra players on top of the 17 above that have trained at some club in England between the ages of 15-21 for 3 years (excluding loans to non-FA clubs, i.e. aborad)
In List A, you can register a further 4 extra players on top of the 21 we're up to so far that are also club trained, meaning they've trained for 3 years at Newcastle United between 15-21, excluding loans to other clubs (even English-clubs, they have to have trained at Newcastle United as their main registered club for 3 of those years).
You don't register Under-21s that qualify as club-trained players, as you can submit them as part of List B for free.
My understanding of the eligibility of Newcastle United's current squad :
Green = Club Trained
Blue = Otherwise locally trained via association
Orange = No special eligibility
Conclusion
Club trained : Only using 2 spots of 4 available which are Sean Longstaff and Joe White, because Miley and Murphy can be submitted in List B as they are under 21 and also club-trained from July 2025.
Locally trained : 18 senior players in total including John Ruddy and Mark Gillespie.
Other : 9 senior players on the books that aren't locally trained players
We can register 23 of 25 List A spots available now, with Lewis Miley and Alex Murphy as part of List B and not taking the club-trained spots of List A.
Sean Longstaff and Joe White take 2 of the 4 club-trained spots for over 21s.
We have 2 free spots on our List A roster for over-21, club-trained players.
Notable players we could sign to pad out our CL2025/2026 squad to 25 players :
Elliott Anderson
Adam Armstrong
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TL;DR
Sean Longstaff currently would occupy a totally free spot for CL2025/2026 with no impact on preventing any other players at Newcastle United from playing in CL2025/2026.
Joe White is in the same situation
We have spots for 2 more 'free' club players, we are using 2 of 4 of the over-21, club-trained player spots
Lewis Miley and other youth team players occupy List B players and do not have to count to the club-trained player spots of List A
Please tell me if I got anything wrong !