There are several mistakes here:

First, you have inherited from "object" and there is no need to explicitly put it, you can leave it empty.

Second, the way you declared your variables in your class makes the class share the same values across all instances, thats why you get the latest modified values always. you should use "self.variable" instead, and declare a constructor function for that.

Third, you are modifying Test1.Dat1 4 times and appending the same object twice. thats why you get the same object every time.

this is the right way:

class TestDat():          # leave this empty
    def __init__(self):   # constructor function using self
        self.Dat1 = None  # variable using self.
        self.Dat2 = None  # variable using self
    
TestArray = [] #empty array

Test1 = TestDat() #this is an object
Test2 = TestDat() #this is another object
        
Test1.Dat1 = 0 #assigning value to object 1 
Test1.Dat2 = 1 #assigning value to object 1 
    
Test2.Dat1 = 3 #assigning value to object 2 
Test2.Dat2 = 4 #assigning value to object 2

TestArray.append(Test1) #append object 1
TestArray.append(Test2) #append object 2 
    
print (TestArray[0].Dat1) # this is Test1
print (TestArray[1].Dat1) # this is Test2

or even simpler:

class TestDat():
    def __init__(self, Dat1, Dat2):
        self.Dat1 = Dat1
        self.Dat2 = Dat2

TestArray = [TestDat(0,1),
             TestDat(3,4)]

print (TestArray[0].Dat1) # this is Test1
print (TestArray[1].Dat1) # this is Test2

or this way:

class TestDat():
    def __init__(self):
        self.Dat1 = None
        self.Dat2 = None
    
TestArray = [] #empty array
size = 2       #number of loops

for x in range(size):  # appending empty objects
    TestArray.append(TestDat())

#initialize later
TestArray[0].Dat1 = 0
TestArray[0].Dat2 = 1

TestArray[1].Dat1 = 3
TestArray[1].Dat2 = 4

print("print everithing")
for x in range(len(TestArray)):
    print("object "+str(x))
    print(TestArray[x].Dat1)
    print(TestArray[x].Dat2)