The Republic of China's government controls the island of Taiwan and a few islands in Fuchien (Fujian) province. Do most proposals for an independent Taiwan call for the ROC controlled parts of Fuchien to become part of Taiwan, to be handed over to PRC control, or some other option?
Taiwan independence supporter here. I'll answer this in two parts.
Part 1: Clarifying misunderstanding
I think there is a misunderstanding in the question's terminologies. You're right that ROC's current jurisdiction covers the Taiwan island and several smaller islands, namely Penghu, Kinmen, and Matsu. For simplicity, these regions are collectively called "Free Areas of Republic of China"
While it is an ironic fact that Kinmen and Matsu are geographically closer to mainland China than Taiwan island, they are legally considered "Counties" under Taiwan the country, not Fujian the province. The concept of "Province" has been defuncted in ROC for a long time as they no longer serve adminsitrative purpose, so when you refer to "Fujian Province", you are referring to an administrative region exclusively under PRC jurisdiction.
Kinmen and Matsu's status as Counties under Taiwan is not just a legal fact but also a political one. The residents of Kinmen and Matsu participate in regular democratic elections just as everyone else closer to the Taiwan island, whereas the residents in Fujian have no election at all, this should demonstrate that geographic proximity does not always imply political jurisdiction.
Part 2: What to do with Kinmen and Matsu after independence
The short answer is there is no plan at the moment.
Kinmen and Matsu exist in a geopolitically awkward position. While they are under ROC jurisdiction for histoircal reasons, the real-life experience of living there could make one feel closer to China than Taiwan. Indeed, both areas have consistently voted for pro-China parties in national and local elections (Note, by "pro-China" I mean the nationalist China, not the communist one that governs PRC today).
There is also a disconnect between people living in these areas compared to those who live closer to Taiwan island. I think residents of Kinmen and Matsu often feel culturally disconnected from residents of Taiwan island and vice versa. I wouldn't say there is antagonism but there is certainly indifference.
On principle, I personally think the issue should be up for the residents of Kinmen and Matsu to decide democratically. There should be a free and fair referendum and the Taiwanese government should honor the will of the residents.
That being said, I really doubt being absorbed into PRC would be an attractive prospect since it means relinquishing basic democratic right. If independence does come to pass one day, I think the most probable outcome is that the Taiwnaese govenrment would devolve significant power to Kinmen and Matsu's local government so they can enjoy regional autonomy (something similar to Åland region in Finland).