It seems that I’ve solved the problem. Found out that attributes introduced in __init__(self,...) should be explicitly annotated the following way:
class MyModule(torch.nn.Module):
    class_field : MyClass
    def __init__(self):
        super().__init__()
        self.class_field = torch.jit.export(MyClass(weights = (1.0, 1.0, 1.0, 1.0,)))                      

Ofk, if they are custom scripted classes.
P.S. The proper way to initialize custom class field is still unclear to me, I mean:
self.class_field = torch.jit.export(MyClass(weights = (1.0, 1.0, 1.0, 1.0,)))

or just
self.class_field = MyClass(weights = (1.0, 1.0, 1.0, 1.0,))

Behaviour is the same