Władysław II Jagiełło, King of Poland and Supreme Duke of Lithuania has a healthly son born in 1408 (instead of daughter Hedwig) named Władysław after father. IOTL Jadwiga/Hedwig was proclaimed heiress to Polish throne in 1413 during congress of Jedlnia. It should be even easier with son (whose mother, unlike OTL fourth wife of Jagiełło, Sonka of Halshany is descendant of Polish kings, granddaughter of Casimir the Great). And Jogaila has another option to secure Polish crown for his son-he only need to make him Grand Duke of Lithuania after Vytautas' death, it is almost guaranteed that Poles would elect to the throne ruler of Lithuania. Jogaila ITTL would never decide to make his brother Švitrigaila Grand Duke after Vytautas if he has adult son by the time of his cousin's death. That's mean trouble with Švitrigaila, but he really troublesome IOTL and would still ally with Teutonic Knights to get Ducal throne for himself. Due to fact that he relied on support of Orthodox Ruthenian population of GDL he'll still be unpopular among Catholic Lithuanians, perhaps ITTL he'll be assassinated successfuly. Question is what would Žygimantas Kęstutaitis do? Would he stay loyal to Jogaila's son? Young Władysław would not have easy life, Švitrigaila's supporters would propably try to assassinate him instead of Žygimantas (unless Švitrigaila is killed earlier, which is IMHO likely), but if he is as capable like OTL Casimir IV he should succeed in his struggle for both thrones, or once elected to Polish throne he'll made someone ( likely Žygimantas or his son Mykolas) his hand in Lithuania keeping title of Supreme Duke?
In Poland last years of Jogaila's rule should be more effective if monarch don't need to put so much energy in securing throne for his son. So less priviledges for nobles and more support for Hussites? And of course after Jogaila's death bishop Zbigniew Oleśnicki would never achieve his OTL position-no need for regency with 26 years old heir to the throne. So Poland would not get closer to Emperor (IOTL hatred towards Hussites and Turks and support for conciliarism in Catholic Church shared by Sigismund of Luxembourg and bishhop Oleśnicki caused shift in Polish foreign politics during miniority of Jogaila's sons, something that would likely not happen ITTL, so maybe campaign to get Czech throne for Jagiellon after Sigismund's death would be more successful ITTL?)
In Poland last years of Jogaila's rule should be more effective if monarch don't need to put so much energy in securing throne for his son. So less priviledges for nobles and more support for Hussites? And of course after Jogaila's death bishop Zbigniew Oleśnicki would never achieve his OTL position-no need for regency with 26 years old heir to the throne. So Poland would not get closer to Emperor (IOTL hatred towards Hussites and Turks and support for conciliarism in Catholic Church shared by Sigismund of Luxembourg and bishhop Oleśnicki caused shift in Polish foreign politics during miniority of Jogaila's sons, something that would likely not happen ITTL, so maybe campaign to get Czech throne for Jagiellon after Sigismund's death would be more successful ITTL?)