Hi Olga,
the form 'littler' does appear in dictionaries such as Oxford etc but its use is very uncommon in British English and virtually unheard of in Ireland where I'm based.
Most native English-speakers around these parts would probably imagine the form to be ungrammatical (the grammatical test in descriptive grammars being what the native-speaker feels is 'sayable'). It would be used mostly by children who have learnt the general grammatical rule for comparatives but haven't latched onto the more common forms: smaller.
I suspect its more or less common use in certain areas is to do with pronunciation issues - it feels like a pronunciation mouthful in certain accents.
Hope this helps,
Bob