Neither is correct.
First of all, on a refinance, if you meet the other rules to deduct points, you must spread them out over the life of the mortgage (such as 360 months for a 30 year mortgage). So assuming you refinanced in June, 2017 and the first payment was due August 1. You paid 5 payments, so your points deduction in 2017 was $16.92. ($1235 divided by 360 x 5 payments).
For 2018 your allowable deduction is $41.17.
(The deduction would be higher for a 15 or 20 year mortgage, of course.)
You can deduct more of the points all at once if you used the proceeds to substantially improve your home. For example, if you refinanced for $123,500 and used $40,000 to remodel the kitchen, you could deduct 32% of the points right away and the rest over the life of the mortgage.
If you later refinance again with a different bank, you can deduct the remaining unused amount of the points all at once in the year you refinance. If you refinance with the same lender, you must add the unused points to any new points and spread them out over the life of the new loan.
You certainly don't deduct the full amount of the points in more than one year.
