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I want to use a built-in function buffer of GeoPandas. I want to create a buffer of 10 centimeters around the original geometry but buffer method take argument in degree, so what value do I need to pass to achieve 10 centimeter buffer for projection of EPSG:4326?

.buffer() takes arguments in degree format only, how can I use meters format? Do I need to change the projection?

df['geometry'].buffer(meter_value)
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Yes you need to reproject into a coordinate system with meters as units.

import geopandas as gpd

df = gpd.read_file(r'C:\GIS\data\tempdata\points_wgs84.shp')
df = df.to_crs(3043) #Pick another
df['geometry'] = df['geometry'].buffer(0.1)
df = df.to_crs(4326) #Back to 4326

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