This is the longest version I found:

PO NÁBREŽÍ KONÍK BEŽÍ
1.
Po nábreží koník beží, koník vraný,
skadiaľže si, šuhajíček, maľovaný?
[:Skadiaľ som, stadiaľ som,
slovenského rodu som, duša moja.:]

2.
Z tej jedličky dve hrdličky na tú lúčku.
Ja som Slovák, ty Slovenka, daj mi rúčku.
[:Rúčku ti podávam,
tebe verná ostávam, duša moja.:]

3.
Pod lipkou, nad lipkou iskierečka,
skadeže si moja milá frajerečka.
[:Skadiaľ som, stadiaľ som,
slovenského rodu som, duša moja.:]

4.
Povedz že mi, duša moja, čia ty budeš,
povedz že mi, duša moja, čia ty budeš?
[:Už som povedala,
že ja budem len tvoja, duša moja.:]

DeepL.com translates it as...

1. A horse is running along the embankment, a wounded horse,
Where did you come from, little painted horse?
[:Where I'm from, where I'm from,
I am of Slovak descent, my soul.]

2. From that fir-tree two doves to that meadow.
I'm Slovak, you're Slovak, give me a hand.
[:I'm giving you my hand,
I remain faithful to you, my soul.]

3. Under the linden tree, above the linden tree,
Where did you come from, my dear little dude?
[:Where I'm from, where I'm from,
I am of Slovak descent, my soul.]

4. Tell me, my soul, here you will be,
Tell me, my soul, will you be here?
[:I have already said,
that I will be yours, my soul.]

There are more videos online if you search with the title of the song.
One with 3 verses only but with an English translation, another sung by the band "Parom".