I might have a half sister, how should I contact her?

I could need some help approaching this situation. I'm 25 f, I grew up in Spain where my parents lived during my childhood but ended up moving to Germany (where my family 's originally from) nine years ago. I'm an only child without a big family. My childhood wasn't always easy as my father was absent most of the time and my mother has some other major issues but our contact has gotten progressively better over the last years.

One year ago, my father casually mentioned he suspected having another child.

Apparently, he dated an older woman around 8-10 years before I was born. He lived in Madrid around that time and was in his early twenties, she was over ten years older than him, single and childfree even though she seemed to want children.

They lost contact and only saw eachother once a couple of years afterwards. He told me the interaction didn't sit right with him. One of the first thing she asked him after a longer period of time without seeing eachother was if he had any children. My father was still very young at that time so he answered he hadn't any. She then immediatly said „well, you probably have some somewhere, you just don't know“.

My father kept having the feeling she might have „used“ him to have a child before it was too late for her.

After some research, I was able to find the woman and her daughter. The daughter's age seems to match the time period and I do see some similarities to my father's facial features. But most important detail is, she only has her mother's surname. In Spain, people have 2 family names: 1st the father's family name, 2nd the mother's family name.

I'm not saying this is a solid proof at all, but I haven't been able to forget about it since.

I am aware that reaching out to her could cause some serious inconveniences but I have struggled with loneliness and family problems my whole live so having a close relative (in case she wished some contact as well) would mean the world to me.

Is it unfair if I try to get in contact?

I'd be thankful for some advice!