The difference between these two words is slight and tricky to understand. They are both adverbs, and have the root of ‘doubt’.
‘Undoubtably’ means ‘in a way that can’t be doubted’.
“Nelson Mandela undoubtably led South Africa towards a brighter future.”
‘Undoubtedly’, on the other hand, means ‘without a doubt’.
“The statements from the Prime Minister are undoubtedly true.”