To be honest, as far as I see, seemingly your question Is a little complex, but I hope to be able to give you some useful information regarding your questions.
Initially, in regard to the meaning of the mentioned word,” Sayyid”:
it can be spelled “Seyyed", "Syed" and "Saiyid" too (which it is
pronounced [ˈsæjjɪd], or [ˈsæjjed], Arabic: سيد; so its meaning is
Mister) (and its plural is Sadah Arabic: سادة, Sādah) which is an
honorific title, it denotes males accepted as descendants of the
Islamic prophet Muhammad through his grandsons, Hasan ibn Ali and also
Hussayn ibn Ali, sons of the daughter of prophet Muhammad( Fatimah)
and his son-in-law Ali (Ali ibn Abi Talib).
In other word, we can mention that all children of Hashim ibn 'Abd Manaf (Arabic: هاشم بن عبد مناف; ca. 464 – 497) (who was the great-grandfather of prophet Muhammad(PBUH)), are Sayyids.
As a brief result:
“Sayyid” means the children of the Prophet(pbuh). So there are many
sources(Sunni) that have pointed regarding the mentioned meaning.
Such as:
1-العلم الظاهر فی نفع النسب الطاهر ابن عابدین ۲- الصواعق المحرقه ابن
حجر هیثمی ۳- شرف الأسباط القاسمی ۴- تذکرة الخواص سبط جوزی ۵- الفصول
رشیدالدین ابوالفضل میبدی حنفی ۶- مطالب السؤال فی مناقب آل الرسول(ص)
محمدبن طلحه شافعی
1-Al elm Zaher fi naf’ e nasab Taher ibn abedin 2-a-savaeq-al-mhraqah
ibn hjr heithami 3-Sharaf-al-esbat alqasemi 4-tazkeratol-khavas
sabt-e-Joozi 5-Al-Fosool 6-mataaleb-o-so’al fi- manaqeb Ale rasul (s)
Muhammad ibn Talha Shafe’i
At the moment, they(Sadah) have not any main place in the world and in fact they are dispersing in many countries. Hence it is not possible to say that all of them are only in a specified country, because of some reasons such as political matters(war,..), economic problems(business, immigration,..), cultural matters(marriage,..) and so on. As mentioned before, they(Sadah) are in many countries such as:
Indonesia, Iran, Iraq, India, Turkey, Lebanon, China, Saudi Arabia, Yemen, Greece and many other countries.
For instance, there are more than 6 million seyyeds (sadah) in Iran, and according to the census, there are approximately 60 million sadat all across the world. Thus we cannot say that majority of them are in a specified country.{1}
{1} - www.farsnews.com
Sources:
solale.ir (in Farsi (Persian))
And also by the help of some other sites (Shia Sites).