To generate test cases for the given problem statement, we need to create random strings \( S \) and \( T' \) that satisfy the constraints. Here is a test case generator for the problem:

```python
import random
import string

def generate_random_string(length):
    return ''.join(random.choices(string.ascii_letters, k=length))

def tcgen():
    # Length of S
    len_S = random.randint(1, 300000)
    
    # Generate random string S
    S = generate_random_string(len_S)
    
    # Length of T' should be at most |S| and at least 1
    len_T_prime = random.randint(1, len_S)
    
    # Generate random string T'
    T_prime = generate_random_string(len_T_prime)
    
    return S, T_prime

# Example usage:
S, T_prime = tcgen()
print(S)
print(T_prime)
```

### Explanation:
- **generate_random_string(length)**: This helper function generates a random string of the given length using uppercase and lowercase letters.
- **tcgen()**: This function generates a random test case:
  - It first determines the length of \( S \) which is a random integer between 1 and 300,000.
  - It then generates a random string \( S \) of that length.
  - It determines the length of \( T' \) which is a random integer between 1 and the length of \( S \).
  - It generates a random string \( T' \) of that length.
  - Finally, it returns the generated strings \( S \) and \( T' \).

By running `tcgen()`, you can generate multiple test cases that adhere to the problem constraints.