I\'m trying to create a scatter plot in Python. I have a dataframe \'df\' with a specified category and x and y are column numbers:
groups = df.groupby(category)         
        
ax.plot does not have x and y arguments. 
The signature is Axes.plot(*args, **kwargs), meaning that x and y are simply positional arguments. If you specify x= and y= they will be treated as keyword arguments and ignored. 
So remove x= and y= from the code, 
ax.plot(group.iloc[:,x], group.iloc[:,y], marker='o', linestyle='',label=name)
Complete example:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
df = pd.DataFrame({"x":np.random.rand(40), 
                   "y":np.random.rand(40),
                   "category": np.random.choice(list("ABCD"), size=40)})
category = "category"
x=1; y=2
groups = df.groupby(category)
fig, ax = plt.subplots()
for name, group in groups:
    ax.plot(group.iloc[:,x], group.iloc[:,y], marker='o', linestyle='',label=name)
fig = ax.get_figure()
#fig.savefig(path)
plt.show()