Szmodics was named in the Ireland squad for two summer internationals, but had to pull out after aggravating a shoulder injury.
And Taylor would have had a great chance of making that squad, but for suffering a hamstring injury in the penultimate game of last season.
Injury and a lack of gametime ruled both of them out of Ireland’s matches in the current international break.
The last player to win a full international cap while playing for Posh was right-back Michael Smith for Northern Ireland in 2016.
Gaby Zakuani’s 20 caps for DR Congo is the most by a serving Posh player.
Here are the Posh internationals...
Injury and a lack of gametime ruled both of them out of Ireland’s matches in the current international break.
5. TONY MILLINGTON
8 caps for Wales. Talented goalkeeper from the 1960s who played at Wembley against England while a Posh player. England won 5-1. A decent servant for Posh in some troubled times, making 132 first-team appearances. Photo by Don Morley/Allsport/Getty Images).
6. ANDRE BOUCAUD
6 caps for Trinidad & Tobago. A gifted midfielder nicknamed ‘The Magician’ because of his wizardry on the ball, although it might also have been because he kept disappearing in games. Only started 36 games for Posh.
7. TREVOR ANDERSON
4 caps for Northern Ireland. An ex-Manchester United winger who was a disappointment at London Road. Scored just seven goals in 58 Posh appearances after scoring twice in 19 games for United. Posh signed him from Swindon.
8. DANNY SONNER
4 caps for Northern Ireland. Midfielder who didn’t make his mark on Posh after a decent career at Ipswich, Sheffield Wednesday and Birmingham City. While at Posh he was recalled by Northern Ireland after a three-year absence.