Pierogi is one of the delicacies of slavic cuisine. Is it true that they are an adaptation from the chinese jiaozi/dumplings? What are the earliest known records about pierogi recipes?

Food history can be snarly--most people have their own family or cultural stories associated with their food, and there's a lot out there that "everyone knows." Sometimes what "everyone knows" even makes it into legitimate published scholarship. In this case, the Oxford Encyclopedia of Food and Drink in America absolutely does say Chinese dumplings/jiaozi are the direct ancestor of the Eastern European pierogi (varnyky, pierozkhi, etc). However, that appears not to be true.

Dumplings, most scholars seem to agree, are a near-ubiquitous food like pancakes are: the concept of dropping a piece of dough in boiling water, the simplest form of "dumpling," is rudimentary and of course exists in countless variations across cultures from West Africa to Southeast Asia. So rudimentary, in fact, that Ukrainian varynky originally just meant "food." And there are all the borderline cases--is gnocchi a noodle or a dumpling? What about Spätzle? To say nothing of what Alan Davidson had to say about the Chinese and Central Asian variety:

English-speakers, seeking a term which could be applied to various kinds of oriental filled pasta, unhappily chose ‘dumpling’, [a] heinous excursion.

But this only gives us the 19th century view, after the word "dumpling" itself had entered into English (17th century). As to a potential genealogical link?

Naomi Guttman and Franklin Sciacca agree that the oldest evidence for dumpling-like food does indeed come from China. In the Song Dynasty (960-1279), sources describe dumplings as an on-the-go snack sold at markets; there is apparently archaeological evidence of dumplings from around 700 in Turpan.

Meanwhile, we don't hear about pirog in Eastern Europe until the 12th century, where it seems to mean a type of bread made from sifted flour--but also to be a more general reference to communal food at a feast. For the idea of a stuffed pierogi, we have to look to Russian sources in the 16th century, where monastic texts delineate which types of fillings are appropriate for fasting days (peas and/or fish, mostly) and inform cooks to use nut oil for the cooking.

But Guttman and Sciacca argue that pierogies had their own genesis in Eastern Europe rather than being a transfer from somewhere East and/or South. They point to the linguistic evidence that pirog comes from bread and from an archaic root for "wheat." Meanwhile, in cases of cultural transfer like stuffed pasta in Italy, there is linguistic evidence to tie ravioli in particular back to Arab-ruled Sicily and from there to Persia.

Well, qualify that. They think pierogies mostly had their own genesis in Eastern Europe. Circling back to the original problem of distinguishing noodles and dumplings, there's a lot of linguistic similarity between, on one hand, Ukrainian and indigenous Siberian names for pasta and pasta dough, and on the other, names in obsolete Turkic languages. So the idea of a development of dumplings out of a more properly "pasta" food brought by Mongol/Tatar invasion or contact seems likely to Guttman and Sciacca.

As to the specific evolution of dumpling-dough into stuffed mini-pies or turnovers into what we know as typical pierogies today, that last step in Poland proper isn't attested until the 19th century! Since they're called pierogi ruskie at that point, the scholars think it's a Polish import from Russian culture.

And to close out with the great legend of pierogies, because of course there is one. St. Jacek/Hyacinth (d. 1257) was a Polish saint who, among other things, is said to have worked a miracle of restoring a grain harvest after the town's (outside Krakow) crops were obliterated by a severe storm in 1238. Well, over the centuries this morphed into the elaboration that he and the townspeople turned the grain into flour, and with the flour they made pierogies to celebrate.

Pierogies might be so basic that their Ukrainian equivalent was just called "food," but they apparently are also so yummy that they developed a reputation as miraculous.