Is Customs Check Required between flights

That can depend on your ticketing, and your baggage.
If your baggage is checked through, and it's an interline connection, then you may not clear customs until your final destination.
It appears, however, that you are making a 2nd booking. That will mean clearing customs at your first point of entry, and checking in anew.

There is immigration, which is the presentation of your passport to an immigration officer, and there is customs, which is typically a rather informal affair involving luggage waived through an arrivals hall at the end point of your journey.

You clear immigration at your first point of entry into the Schengen Zone, which is slightly different than the EU membership zone. If you fly into a place like Amsterdam or Paris, they are both Schengen, you clear immigration and your subsequent flights within the Schengen zone to Spain are pretty much treated like a US domestic route. If you fly into the UK, which is not part of Schengen zone, and you're on a single connecting ticket, you follow directions for international transit instead of clearing immigration there, and will instead go through immigration & customs in Spain.

If you're arriving at a non-Schengen country on one ticket and then entering a Schengen country on another ticket, it gets tricky and you should have a huge time buffer, especially when you're talking airlines that don't interline bags with each other and you might have to clear immigration in the non-Schengen country before getting on the next flight to Spain.

To clarify, you NEVER go through customs, your luggage does. Customs is the check of what your luggage contains, if it is allowed into the country and if any taxes are to be paid on it.

You go through immigration (aka passport control), which is where they inspect your passport, decide if you are allowed into the country and possibly stamp your passport.
You go through immigration when you enter the Schengen Area, which if your layover is in the Schengen Area will be there, if it is not then you enter the Schengen Area when you land in Spain.

Assuming this is one through booking, your luggage will be labelled through to your final destination in Spain, and you will not see it until then. You then carry your luggage through customs, which is a random check only (less than 1% of luggage checked).

Thank you for the very helpful information. I appreciate it.