Я ищу долгосрочных отношений
Отношения (in the sense of "romantic relationship") is plural in Russian, it's idiomatic.
In the singular, отношение means "relation" in the context of math, relational theory and the like. It can also mean "attitude", "respect" and has some other meanings as well, none of which apply to romantic relationships.
The verb искать takes both the genitive and the accusative, but the accusative implies definiteness, like in "I'm looking for the romantic relationship" in English. It's one of the rare cases where the concept of definiteness is syntactically evident in Russian. Since definiteness makes little sense here, you should use the genitive.
Finally, ищу чего-то is a viable but not quite idiomatic way of saying "I'm looking for" in Russian, unless you're actually searching for a physical object.
Depending on the context, it might be better to say надеюсь на долгосрочные отношения, жду долгосрочных отношений, нацелен на долгосрочные отношения etc.