The first one is actually a Daihatsu oil filter part no. but can you tell which company made this i.e. anything written on it? You might be using a local made or Chinese made replacement filter unless this is the "Made in Japan" filter you talked about and is the actual Daihatsu OEM oil filter? I am also unable to find anything about the 90915-YZZC5 filter you have been informed about. It should have come up under the Oil Filter cross reference website but it is not giving any info so not sure what to make of it.
When you give "15601-87204" under Oil filter cross reference site, it gives both the 90915-10003 (Jap made) and 90915-YZZE1 (Thai made) filter as compatible. If you can confirm they will fit and work on your engine then go for whichever suits your budget. I will suggest you refrain from using some unknown oil filter. We all pay top amount for synthetic oil, why not go with a good oil filter too?
In end, I would like to clarify one thing that I am not an expert in suggesting a filter for your engine. I honestly don't know much other than a few searches here and there about your car and its engine. None of which turned up much information about the exact part no. of oil filter recommended by Daihatsu. Does Toyota service Daihatsu vehicles? If you can confirm this from a Toyota Dealership/3S then go there and ask which Toyota filter will fit.
@Xulfiqar, can you please guide us about this.