I need to have a caste that is only slightly different from the normal male caste. How can I set it the correct way in priority so that my caste takes priority over the normal male caste?

SP > Caste Options > (name of your caste) > Caste: Priority > and set it to any value that is higher than the Priority setting of your Male caste. By default that probably means higher than 0.

Just to explain what this means, if a sim is in both castes AND if both castes have different explicitly defined settings for any of their Caste Options, then the caste with the higher priority will win out for each such option.

Yes,set the number higher.
As an example, if you name your castes including the priority no, you can see directly how the order is,

for the sorting and maybe also add a M for manual, all others are automatic, which will be the most I guess like
001p_name_M
050p_name
095p_name
140p_name_M
untill 999 this should be high enough.

when you change a priority, remember to change the name too.

This is my way, and it was helping me a lot to understand the priority system.
Otherwise you always have to go into each caste setting to see what number it has.
Leave some numbers free in-between, so you can add easily new ones.

There is also a hierarchy between caste types
the right overwrites the left
Town, Lot, Household, Sim

Thanks guys