The verse is not extant in the manuscripts of the Padma Purana which are known today, but the verse was quoted in some of the books of the Hindu authors from the previous centuries.
Thus in the Prameya Ratnavali of Baladeva Vidyabhushana, a Gaudiya Vaishnava author and acarya, he quoted that verse:
yad uktam padma-purane
mantras te nishphala matah
atahh kalau bhavishyanti
catvaras te kalau bhavya
hy utkale purushottamat
yat—which; uktam—is spoken; padma-purane—in the Padma Purana; sampradaya-vihinah—those who are not connected to the bona-fide disciplic succession; ye—those who; mantrah—mantras; te—they; nishphalah—without result; matah—are considered; atah—for this reason; kalau—in the age of Kali; bhavishyanti—there will be; catvarah—four; sampradayah—bona-fide disciplic successions; shri—from Lakshmi-devi; brahma—from Lord Brahma; rudra—from Lord Shiva; sanakah—and from Sanaka and the Kumara sons of Brahma; vaishnavah—in relation to Lord Vishnu; kshiti—the world; pavanah—purifying; catvarah—four; te—they; kalau—in the age of kali; bhavyah—will be; hi--indeed; utkale—in Orissa; purushottamat—from Jagannatha Puri.
The Padma Purana explains: "Unless one is initiated by a bona-fide spiritual master in the disciplic succession, the mantra he might have received is without any effect. For this reason four Vaishnava disciplic successions, inaugurated by Lakshmi-devi, Lord Brahma, LordShiva, and the four Kumaras, will appear in the holy place of Jagannatha Puri, and purify the entire earth during the age of Kali."
ramnujam shrih svi-cakre
ramanujam—Ramanuja; shrih—Lakshmi-devi; svi-cakre—selected; madvacaryam—Madhvacarya; caturmukah—Lord Brahma; shri-vishnu-svaminam—Vishnu Svami; rudrah—Lord Shiva; nimbadityam—Nimbarka; catuhsanah—the four Kumaras.
Lakshmi-devi chose Ramanujacarya to represent her disciplic succession. In the same way Lord Brahma chose Madhvacarya, Lord Shiva chose Vishnu Svami, and the four Kumaras chose Nimbarka.