Hi
Patriarchy and paternalism are two different things.
Patriarchy is, broadly speaking, the hierarchical social system which gives men power over women in society. This does not need to be interpreted as literal power, although it has its roots in legal systems which saw women as men’s property, but can include ways of organising which have grown up along male lines - so for example, the idea that we work full-time all our lives to accrue social and financial capital does not account for maternity and childcare which are biologically and traditionally seen as the role of women. Patriarchy is also hierarchical for men, given how power and status in society is constructed economically and politically. This is what people mean when they say patriarchy harms men too.
Paternalism is top down decisions about the welfare of others, broadly speaking, and because of how society is organised, these are usually men making these decisions. It may come with reciprocal obligations, so for example, an industrialist in the past may have provided housing and education for his employees but expected that they attend church and don’t get drunk outside of work. It comes from paternal, so the obligations of a father. Maternalist is about protecting the welfare of mothers and children, I think.
No idea if that is any help, but that is how I have understood the concepts.