Fraction of hot blini cooked with bit of lox inside (9)

'fraction' is the definition.
(billionth is a kind of fraction)

'blini cooked with bit of lox inside' is the wordplay.
'cooked with' is an anagram indicator.
'bit' suggests taking the first letters (I've seen 'bits of' mean this).
'inside' becomes 'th' (I can't explain this - if you can you should believe this answer much more).
The first letters of 'of lox' is 'ol'.
'blini' anagrammed with 'ol' gives 'billion'.
'billion'+'th'='BILLIONTH'

'of hot' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.