Seve,
No, it's not.
The relative pronoun 'which' is correct in your sentence.
I have received an invoice of $100 on WHICH I had to pay $20 of tax.
'Which' refers to the "invoice of $100".
"What" can be used as a relative pronoun but it can never refer to a noun or pronoun that comes before it.
$20 is what I paid on the invoice of $100.......................correct
$20 is the amount what I paid on the invoce of $100....incorrect
$20 is the amount that I paid on the invoice of $100.....correct
I already spent what I earned last month......correct
Nothing can change the destiny what is mine.....incorrect
Nothing can change the destiny (which or that) is mine....correct
Love is what can change my destiny..........correct