If we send out a statement every month due to electronic funds transfers from a savings account, does my statement cycle change to six a month or does it stay six per quarter since the true cycle is quarterly for the number of allowed withdrawals?

We have to monitor excess debits on a four-week (monthly) cycle. If you want to be more restrictive and limit transactions on savings/MMDAs to six per quarter, you can do so.

Brenda's right. Even if you statement cycle is quarterly, you can still allow 6 per month.

Then the question is: If the customer does more than 6 excessive transactions per month, but receives the statements every quater, does it mean you send only one letter per quater (even though it will be over 20 transactions during this particular quater)?
And then second question i have is that required to send out a statement every month due to electronic funds transfers from a savings account? Can the bank send statements once per quater?

No. Track (and manage) excess debits on monthly basis.

You can send quarterly statements as a rule, but you must provide monthly statement if any electronic debits have occurred (Reg E).

Can you explain then smth to me: if the customer does not get statement until end of march (end of 1st quater), for example, you send him a letter about excessive transactions in January during first week of February, then second letter in the beginning of March for the month of February, and by the time he gets his statement for the 1st quarter, you send him the 3rd and final letter?

If he violates the excess debit rules in Jan, Feb and Mar, he has hit his third violation period and you should take steps to convert or close the account. If he has 21 pre-authorized debits to a savings account in one quarter, obviously it isn't the right account for that customer.

Znatok - In that situation, I would also print out their account activity for the period you are sending them a letter for. I usually number all of the limited transactions to show the customer what is considered a violation.