regex or does not work - I do not know what is wrong in my pattern

You can combine the expressions you want to match with a simple | but remember that the engine will always prefer the first possible match; so you want to put the more specific patterns first, and then fall back to the more generic cases.

Try this:

my_re = re.compile(r'^([0-9]{4}-[0-9]{2}-[0-9]{2,}|\d+|N(?:aN|one)|)(\D.*)$', re.IGNORECASE)

The re.IGNORECASE flag says to ignore case differences.

Also, note that the quantifier {0,} is better written *; but you want to require at least one match, or then fall back to a more generic pattern, so actually you want + (which could also be written {1,}; but again, prefer the more succinct standard notation). There is no need for square brackets around \D which already encapsulates a character class (but if you want to cobine two character classes, like [-\d], you do need the square brackets).

Demo: https://ideone.com/Qwp5ao

Finally, note that the standard Python notation for naming local variables prefers snake_case over dromedaryCase. (See also Wikipedia.)

What about the following with re.I:

(None|NaN?|[-\d]+)?(.*)

https://regex101.com/r/d4XPPb/3

Explanation:

• (None|NaN?|[-\d]+)?
  • Either None
  • Or NaN from which the last N is optional (due to ?) so it also matches NA
  • Or digits and dashes one or more times
  • The whole group () is optional due to ? which means it might not be there
• (.*) Any character to the end

However, there can still be edge cases. Consider the following:

National Geographic
---Test

would be parsed as

[Na][tional Geographic]
[---][Test]

An alternative:

From here we can keep on making the regex more complex, however, I think that it would be a lot simpler for you to implement custom parsing without regex. Loop characters in each line and:

• if it starts with digit, parse all digits and dashes into group 1, the rest in group 2 (ie when you hit a character, change group)
• Take the first 4 chars of the string and if they are "none", split them out. At the same time ensure that the 5th character is Upper case (case insensitive line[:4].lower() == "none" and line[4].isupper())
• Similar to the above step but for NA and NaN:
  • line[:3].lower() == "nan" and line[3].isupper()
  • line[:2].lower() == "na" and line[2].isupper()

The above should produce more accurate result and should be a lot easier to read.

Example code:

with open("/tmp/data") as f:
    lines = f.readlines()

results = []
for line in lines:
    # Remove spaces and \n
    line = line.strip()
    if line[0].isdigit() or line[0] == "-":
        i = 0
        while line[i].isdigit() or line[i] == "-":
            i += 1
            if i == len(line) - 1:
                i = len(line)
                break
        results.append((line[:i], line[i:]))

    elif line[:4].lower() == "none" and line[4].isupper():
        results.append((line[:4], line[4:]))

    elif line[:3].lower() == "nan" and line[3].isupper():
        results.append((line[:3], line[3:]))

    elif line[:2].lower() == "na" and line[2].isupper():
        results.append((line[:2], line[2:]))
    else:
         # Assume group1 is missing! Everything is group2
         results.append((None, line))

for g1, g2 in results:
    print(f"[{g1 or ''}][{g2}]")

Data:

$ cat /tmp/data 
2020-10-2125Chavez and Sons
2020-05-02Bean Inc
NaNRobinson, Mcmahon and Atkins
2020-04-25Hill-Fisher
2020-04-02Nothing and Sons
52457Carpenter and Sons
0Carpenter and Sons
Carpenter and Sons
NoneEconomy and Sons
NoNeEconomy and Sons
2020-04-02
NAEconomy and Sons
---Test
National Geographic

Output:

$ python ~/tmp/so.py 
[2020-10-2125][Chavez and Sons]
[2020-05-02][Bean Inc]
[NaN][Robinson, Mcmahon and Atkins]
[2020-04-25][Hill-Fisher]
[2020-04-02][Nothing and Sons]
[52457][Carpenter and Sons]
[0][Carpenter and Sons]
[][Carpenter and Sons]
[None][Economy and Sons]
[NoNe][Economy and Sons]
[2020-04-02][]
[NA][Economy and Sons]
[---][Test]
[][National Geographic]