YP railcard T+C's say:
Minimum fares / Time restrictions
Travelling before 10am minimum fares:
This applies to all tickets except the Off-Peak Day Travelcard (All Zones only) which has separate minimum fare conditions. On or before 10am Monday to Friday (except Public Holidays and during July and August) there is a minimum fare that applies to all purchases with a Young Persons Railcard. This is either £8.00 or £16.00 depending on the type of ticket being purchased. Most will be £8.00, but the following ticket types have a minimum fare of £16.00: Standard Day Returns, Standard Open Returns, European Open Returns.
For example: If an undiscounted Single ticket costs £8.50 and the normal 1/3 discount makes the fare £5.60, you will have to pay the minimum fare of £8.00.
If an undiscounted Standard Open Return costs £27.00, then you will get the full 1/3 discount as the discounted fare of £17.80 is higher than the £16.00 minimum fare.
If you travel regularly before 10am, then a weekly or monthly season ticket may be more appropriate.
Off-Peak Day Travelcards (All Zones only):
Before 10am Monday to Friday (except Public Holidays and in July and August) the minimum fare is £8.00. At and after 10am on Monday to Friday and as advertised on Saturdays, Sundays, Public Holidays and during July and August the minimum fare is £4.80.