When the Americas were discovered many plants were brought back to Europe. For example: potato, tomato, strawberries, chilies etc. At the same time many animals were brought to the Americas including: horses, cattle, sheep, and camels. It seems from the records that there were relatives of these animals in the Americas — for example llamas are in the same family (Camelidae) as camels. I wonder if there were relatives of these vegetables from the Americas already present in Europe or anywhere else in the old world.
Three of your examples: potato, tomato, and chilies, are from the genus Solanum. Along with the rest of the Solanaceae family, they are most diverse in the Americas but some species are found worldwide.
Species that would be found originally in the 'old world' from the Solanum genus and Solanaceae family include the black nightshade, bittersweet nightshade, and deadly nightshade. There is also at least one cultivated plant variously known as eggplant, aubergine, or brinjal (Solanum melongena) that is thought to have been domesticated in Asia.
The strawberry genus, Fragaria, also has species world-wide.
Of course, because all life on Earth is related, the answer to the general question "are there relatives of X found in some place" will always be "yes" as long as there is life there, it's only a matter of the extent of relation.