I have a/the father suffering from leukemia.

[taked4700]

Thank you, bhaisahab, 5jj and Emsr2d2.

Sorry for my posting in a row. I'm not intending to induce you to take care of the maze of my misunderstanding.

So, let me make sure once again.

"I have the/a book that you said you lost the other day."

In this context both articles make sense.
'A book' implies that you lost more than one book.
'The book' means that you lost only one book the other day.

Am I right?

Thanks in advance.

[emsr2d2]

Both are possible but "the" is more likely in this context because it is very likely that the person only told you about one specific book that they had lost.