In Python, how to know whether a string contain a jump substring. like 'abcd' contain 'ad'

You can create an iterator from the test string and validate that every character in the subsequence can be found in the sequence of characters generated by the iterator:

def is_subsequence(a, b):
    seq = iter(b)
    return all(i in seq for i in a)

so that:

print(is_subsequence('ad', 'abcd'))
print(is_subsequence('adc', 'abcd'))

outputs:

True
False

Demo: https://ideone.com/jGdpis