Learn גמרא שבת דף כא: “ת”ר מצות חנוכה (two dots) until “אמר רבה”
https://hebrewbooks.org/shas.aspx?mesechta=2&daf=21b&format=pdf
Learn תוס’ “והמהדרין
Learn רמב”ם ה’ חנוכה פרק ד הלכה א-ב
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=374
Clarify the difference between Tosfos and Rambam
Questions:
What is the reason to light extra candles – Mehadrin and Mehadrin min Hamehadrin?
If someone forgot to add an extra candle for that night of chanukah and only realised later that evening
Should he light an additional candle?
Should he make a bracha when lighting that candle?
Should he light it even if the other candles have already gone out?
See מגן אברהם ס’ תרנ”א ס”ק כ”ה
https://hebrewbooks.org/pdfpager.aspx?req=14327&st=&pgnum=399
See פרי חדש ס’ תרע”ב
See בית יוסף ס’ תרע”ב בשם אורחת חיים
https://hebrewbooks.org/pdfpager.aspx?req=14268&st=&pgnum=602
See שו”ת רע”א תניינא ס’ י”ג
https://hebrewbooks.org/pdfpager.aspx?req=1162&st=&pgnum=10