I'm assuming the algoseek NDX options data includes options
that expire on every trading day as these became available by the end of 2022.

Referring to the Index Options table for the Supported Assets.
https://www.quantconnect.com/docs/v2/writing-algorithms/datasets/algoseek/us-index-options#08-Supported-Assets
The table specifies the NDX NDXP target ticker only has standard
contracts tradable on expiration day and
specifies the NDX NQX target ticker has standard and weekly contracts that
are tradable on expiration day.

Using the NDX NQX target ticker this only returns the Weekly Fri 0DTE expirations
and the Monthly 0DTE expirations. It does not return any other 0DTE expirations for
the other week days.
There are also periods of completely missing chain data for weekly and monthly.
Log extracts:

2023-01-03 09:31:00 :  2023-01-03 09:31:00 empty
2023-01-04 09:31:00 :  2023-01-04 09:31:00 empty
2023-01-05 09:31:00 :  2023-01-05 09:31:00 empty
2023-01-06 09:31:00 :  2023-01-06 09:31:00 OK
2023-01-06 16:19:00 :  2023-01-06 16:19:00 OK
2023-01-09 09:31:00 :  2023-01-09 09:31:00 empty
2023-01-10 09:31:00 :  2023-01-10 09:31:00 empty
2023-01-11 09:31:00 :  2023-01-11 09:31:00 empty
2023-01-12 09:31:00 :  2023-01-12 09:31:00 empty
2023-01-13 09:31:00 :  2023-01-13 09:31:00 OK
2023-01-13 16:19:00 :  2023-01-13 16:19:00 OK
2023-01-17 09:31:00 :  2023-01-17 09:31:00 empty
2023-01-18 09:31:00 :  2023-01-18 09:31:00 empty
2023-01-19 09:31:00 :  2023-01-19 09:31:00 empty
2023-01-20 09:31:00 :  2023-01-20 09:31:00 OK
2023-01-20 16:19:00 :  2023-01-20 16:19:00 OK
2023-01-23 09:31:00 :  2023-01-23 09:31:00 empty
2023-01-24 09:31:00 :  2023-01-24 09:31:00 empty

But when using the NDX NDXP target ticker this returns daily 0DTE expiration contracts,
except for the dates of the standard monthly contract expirations,
which return no chain data on the monthly expiration day.
This doesn't seem to match the supported assets table specification as
it looks to include the weekly pm settled options which expire every day,
which isn't specified in the table, and it seems that the standard monthly contracts
are not tradable on expiration day.
Log extracts:
2023-01-20 09:31:00 :  2023-01-20 09:31:00 empty
2023-02-17 09:31:00 :  2023-02-17 09:31:00 empty
2023-03-17 09:31:00 :  2023-03-17 09:31:00 empty
2023-04-21 09:31:00 :  2023-04-21 09:31:00 empty
2023-05-19 09:31:00 :  2023-05-19 09:31:00 empty
2023-06-16 09:31:00 :  2023-06-16 09:31:00 empty
2023-07-21 09:31:00 :  2023-07-21 09:31:00 empty
2023-08-18 09:31:00 :  2023-08-18 09:31:00 empty

Is it possible to fully access NDX 0DTE options that
are tradable every day including the monthly expirations ?

I noticed there have been some fixes applied for NDX NQX weekly option access
but it seems there are still issues as above.
https://github.com/QuantConnect/Lean/issues/7801

Any info appreciated.
Many thanks.